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uoLfysmohE845tfWlh3rsa0w2w9jx3ff4dg | physics | capacitor | capacitors-with-dielectric | Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance
d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and
dielectric constants K<sub>1</sub>, K<sub>2</sub> and K<sub>3</sub>. The first capacitor is fille... | [{"identifier": "A", "content": "$${{{E_1}} \\over {{E_2}}} = {{\\left( {{K_1} + {K_2} + {K_3}} \\right)\\left( {{K_2}{K_3} + {K_3}{K_1} + {K_1}{K_2}} \\right)} \\over {{K_1}{K_2}{K_3}}}$$"}, {"identifier": "B", "content": "$${{{E_1}} \\over {{E_2}}} = {{{K_1}{K_2}{K_3}} \\over {\\left( {{K_1} + {K_2} + {K_3}} \\right)... | ["D"] | null | $${1 \over {{C_1}}} = {d \over {3A{\varepsilon _0}}}\left( {{1 \over {{K_1}}} + {1 \over {{K_2}}} + {1 \over {{K_3}}}} \right)$$<br><br>
$${C_1} = {{3A{\varepsilon _0}\left( {{K_1}{K_2}{K_3}} \right)} \over {d\left( {{K_1}{K_2} + {K_2}{K_3} + {K_3}{K_1}} \right)}}$$<br><br>
$${C_2} = {{A{\varepsilon _0}} \over {3d}}\le... | mcq | jee-main-2019-online-12th-april-morning-slot | 9,291 |
Hqztj32RwUv4gdbjQCirt | physics | capacitor | capacitors-with-dielectric | The parallel combination of two air filled
parallel plate capacitors of capacitance C and
nC is connected to a battery of voltage, V. When
the capacitors are fully charged, the battery is
removed and after that a dielectric material of
dielectric constant K is placed between the two
plates of the first capacitor. The n... | [{"identifier": "A", "content": "V"}, {"identifier": "B", "content": "$${V \\over {K + n}}$$"}, {"identifier": "C", "content": "$${{(n+1)V} \\over {K + n}}$$"}, {"identifier": "D", "content": "$${{nV} \\over {K + n}}$$"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264396/exam_images/y2xokb3qgd0nfpixreoq.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th April Evening Slot Physics - Capacitor Question 101 English Explanation">
Initially Q = CV(1 +... | mcq | jee-main-2019-online-9th-april-evening-slot | 9,292 |
xbp6HGKNkllEQXwKNxCoM | physics | capacitor | capacitors-with-dielectric | Voltage rating of a parallel plate capacitor is
500V. Its dielectric can withstand a maximum
electric field of 10<sup>6</sup> V/m. The plate area is
10<sup>–4</sup> m<sup>2</sup>. What is the dielectric constant is the
capacitance is 15 pF?
(given $$\varepsilon $$<sub>0</sub> = 8.86 × 10<sup>–12</sup> C<sup>2</sup>/Nm<... | [{"identifier": "A", "content": "8.5"}, {"identifier": "B", "content": "4.5"}, {"identifier": "C", "content": "3.8"}, {"identifier": "D", "content": "6.2"}] | ["A"] | null | A = 10<sup>–4</sup> m<sup>2</sup><br><br>
E<sub>max</sub> = 10<sup>6</sup> V/m<br><br>
C = 15 $$\mu $$F<br><br>
$$C = {{k{\varepsilon _0}A} \over d};{{Cd} \over {{\varepsilon _0}A}} = k$$<br><br>
$$k = {{15 \times {{10}^{ - 12}} \times 500 \times {{10}^{ - 6}}} \over {8.86 \times {{10}^{ - 12}} \times {{10}^4}}}$$<br><... | mcq | jee-main-2019-online-8th-april-morning-slot | 9,293 |
Ws750gZXbfcNAbVTbt2LD | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is : | [{"identifier": "A", "content": "508 pJ"}, {"identifier": "B", "content": "692 pJ"}, {"identifier": "C", "content": "560 pJ"}, {"identifier": "D", "content": "600 pJ"}] | ["A"] | null | Initial energy of capacitor
<br><br>U<sub>i</sub> = $${1 \over 2}$$ $${{{v^2}} \over c}$$
<br><br>= $${1 \over 2}$$ $$ \times $$ $${{120 \times 120} \over {12}}$$ = 600 J
<br><br>Since battery is disconnected so charge remain same.
<br><br>Final energy of capacitor
<br><br>U<sub>f</sub> = $${1 \over 2}{{{v^2}} \over ... | mcq | jee-main-2019-online-10th-january-evening-slot | 9,294 |
vP0XhVtnogVRDnetKtpAr | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor is of area 6 cm<sup>2</sup>
and a separation 3 mm. The gap is filled with three dielectric
materials of equal thickness (see figure) with dielectric constants K<sub>1</sub> = 10, K<sub>2</sub> = 12 and K<sub>3</sub> = 14. The dielectric constant of a material which when fully inserted in abo... | [{"identifier": "A", "content": "12"}, {"identifier": "B", "content": "36"}, {"identifier": "C", "content": "14"}, {"identifier": "D", "content": "4"}] | ["A"] | null | Let dielectric constant of material used be K.
<br><br>$$ \therefore $$ $${{10{ \in _0}\,A/3} \over d} + {{12{ \in _0}\,A/3} \over d} + {{14{ \in _0}\,A/3} \over d} = {{K{ \in _0}A} \over d}$$
<br><br>$$ \Rightarrow $$ K $$=$$ 12 | mcq | jee-main-2019-online-10th-january-morning-slot | 9,295 |
Q6Zn8be4nhNHOsXg9hLxr | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor with square plates is filled with four dielecytrics of dielectrics constants K<sub>1</sub>, K<sub>2</sub>, K<sub>3</sub>, K<sub>4</sub> arranged as shown in the figure. The effective dielectric constant K will be :
<br/><br/><img src="data:image/png;base64,UklGRvoMAABXRUJQVlA4IO4MAAAw1gCdASo... | [{"identifier": "A", "content": "$$K = {{{K_1}{K_2}} \\over {{K_1} + {K_2}}} + {{{K_3}{K_4}} \\over {{K_3} + {K_4}}}$$"}, {"identifier": "B", "content": "$$K = {{\\left( {{K_1} + {K_2}} \\right)\\left( {{K_3} + {K_4}} \\right)} \\over {2\\left( {{K_1} + {K_2} + {K_3} + {K_4}} \\right)}}$$"}, {"identifier": "C", "conten... | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l8p783x6/9aaa2160-762b-467b-9b6f-77cb2867b5bd/32a183a0-4123-11ed-8a36-9f4a474c8481/file-1l8p783x7.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l8p783x6/9aaa2160-762b-467b-9b6f-77cb2867b5bd/32a183a0-4123-11ed-8a36-9f4a474c8481/fi... | mcq | jee-main-2019-online-9th-january-evening-slot | 9,296 |
kz747Ju66OhfUbpOVe7k9k2k5dtgzil | physics | capacitor | capacitors-with-dielectric | <img src="data:image/png;base64,UklGRjAFAABXRUJQVlA4ICQFAAAwJgCdASqlALIAPm0yl0ckIyKhKBH66IANiWlu4J+dnMpu8b/3PtN/vvSJ+jvZ70m2bf8z/N/cj+R/3n+AbZV3gHc75A/QrxAf5X+M+B7/M+hr+mHsRwWv069Wr4j/vPrm+kv0y9l79H/Zr84Ax99fr9fr8whRv+nKNt+YNpb/hsTjjvlXDT++wzkPyLfdpVVqboOoizzqr9NPQyhcCmIog2qJoiUi8yBMeaESYJOSHtvEwOOYea2N4YllCIuVt+tgjiRa... | [{"identifier": "A", "content": "$${{A{ \\in _0}K} \\over d}\\left( {1 + {{\\left( {{{\\alpha d} \\over 2}} \\right)}^2}} \\right)$$"}, {"identifier": "B", "content": "$${{A{ \\in _0}K} \\over d}\\left( {1 + {{\\alpha d} \\over 2}} \\right)$$"}, {"identifier": "C", "content": "$${{A{ \\in _0}K} \\over d}\\left( {1 + {{... | ["B"] | null | k(x) = K(1 + $$\alpha $$x)
<img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267188/exam_images/dgxbiq1c2jogdfyqnrfr.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 7th January Morning Slot Physics - Capacitor Question 96 English Explan... | mcq | jee-main-2020-online-7th-january-morning-slot | 9,298 |
keWX4d3EehQ4aRsXhq1kmhoh7pt | physics | capacitor | capacitors-with-dielectric | For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $${3 \over 4}$$d, where 'd' is the separation between the plates of parallel plate capacitor. The new ... | [{"identifier": "A", "content": "$$C' = {{3 + K} \\over {4K}}{C_0}$$"}, {"identifier": "B", "content": "$$C' = {{4 + K} \\over {3}}{C_0}$$"}, {"identifier": "C", "content": "$$C' = {{4K} \\over {K + 3}}{C_0}$$"}, {"identifier": "D", "content": "$$C' = {{4} \\over {3 + K}}{C_0}$$"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264082/exam_images/b5etp3tyjqbdfjzwwg4i.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 16th March Morning Shift Physics - Capacitor Question 79 English Explanation">
<br>$${C_0} = {{{ ... | mcq | jee-main-2021-online-16th-march-morning-shift | 9,300 |
EYiu0hIf5D4ntdlTFE1kmipv6lt | physics | capacitor | capacitors-with-dielectric | In a parallel plate capacitor set up, the plate area of capacitor is 2 m<sup>2</sup> and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m<sup>2</sup> (see fig.) the capacitance of the set-up will be __________$$\varepsilon $$<sub>o</s... | [] | null | 3 | $${C_1} = {{K{\varepsilon _0}A} \over {d/2}};{C_2} = {{{\varepsilon _0}A} \over {d/2}}$$<br><br>$${1 \over C} = {1 \over {{C_1}}} + {1 \over {{C_2}}} = {d \over {2K{\varepsilon _0}A}} + {d \over {2{\varepsilon _0}A}}$$<br><br>$${1 \over C} = {d \over {2{\varepsilon _0}A}}\left( {{{K + 1} \over K}} \right)$$<br><br>$$C ... | integer | jee-main-2021-online-16th-march-evening-shift | 9,301 |
2kLDoXW2nmibBlsIyh1kmkrvbcb | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor has plate area 100 m<sup>2</sup> and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.<br/><br/>The value of $$\varepsilon $$<sub>0</sub> = 8.85 $$\times$$ 10<... | [] | null | 161 | Area = 100 m<sup>2</sup>
<br><br>Separation (d) = 10 m
<br><br>Thickness = 5 m
<br><br>Dielectric constant (K) = 10
<br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264372/exam_images/seugbn3rslsguohlfjs9.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="J... | integer | jee-main-2021-online-18th-march-morning-shift | 9,302 |
1krw932h9 | physics | capacitor | capacitors-with-dielectric | If q<sub>f</sub> is the free charge on the capacitor plates and q<sub>b</sub> is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge q<sub>b</sub> an be expressed as : | [{"identifier": "A", "content": "$${q_b} = {q_f}\\left( {1 - {1 \\over {\\sqrt k }}} \\right)$$"}, {"identifier": "B", "content": "$${q_b} = {q_f}\\left( {1 - {1 \\over k}} \\right)$$"}, {"identifier": "C", "content": "$${q_b} = {q_f}\\left( {1 + {1 \\over {\\sqrt k }}} \\right)$$"}, {"identifier": "D", "content": "$${... | ["B"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264435/exam_images/jch6clzucnu6f7avkmky.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264336/exam_images/anrb6frpprxszrxdsnpc.webp"><source media="(max-wid... | mcq | jee-main-2021-online-25th-july-evening-shift | 9,304 |
1kryuv6nc | physics | capacitor | capacitors-with-dielectric | In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :<br/><br/>(Given area of plate = A)<br/><br/><img src="data:image/png;base64,UklGRl4JAABXRUJQVlA4IFIJAAAQPwCdASrwAMwAPm0ylkckIyIhJ... | [{"identifier": "A", "content": "$${{15} \\over {34}}{{K{\\varepsilon _0}A} \\over d}$$"}, {"identifier": "B", "content": "$${{15} \\over 6}{{K{\\varepsilon _0}A} \\over d}$$"}, {"identifier": "C", "content": "$${{25} \\over 6}{{K{\\varepsilon _0}A} \\over d}$$"}, {"identifier": "D", "content": "$${9 \\over 6}{{K{\\var... | ["A"] | null | $${1 \over {{C_{eff}}}} = {d \over {K{ \in _0}A}} + {{2d} \over {3K{ \in _0}A}} + {{3d} \over {5K{ \in _0}A}}$$<br><br>$${C_{eff}} = {{15K{\varepsilon _0}A} \over {34d}}$$ | mcq | jee-main-2021-online-27th-july-morning-shift | 9,305 |
1ks180mvi | physics | capacitor | capacitors-with-dielectric | A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be <br/><br/><img src="data:image/png;base64,UklGRlwYAABXRUJQVlA4IFAYAACwhgCdASrAASEBPm0ylkikIqIhI1IaMIANiWlu/H... | [{"identifier": "A", "content": "$${\\tan ^{ - 1}}\\left[ {{q \\over {mg}} \\times {{{C_1}({V_2} - {V_1})} \\over {({C_1} + {C_2})(d - t)}}} \\right]$$"}, {"identifier": "B", "content": "$${\\tan ^{ - 1}}\\left[ {{q \\over {mg}} \\times {{{C_2}({V_2} - {V_1})} \\over {({C_1} + {C_2})(d - t)}}} \\right]$$"}, {"identifie... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264925/exam_images/euz12vdkiqgvti3surfu.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 27th July Evening Shift Physics - Capacitor Question 67 English Explanation 1"><br>Let E be electr... | mcq | jee-main-2021-online-27th-july-evening-shift | 9,306 |
1ktbocpt5 | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K<sub>1</sub> and K<sub>2</sub> of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:<br/><br/><img src="data:image/... | [{"identifier": "A", "content": "$${{{\\varepsilon _0}A} \\over d}\\left( {{1 \\over 2} + {{{K_1}{K_2}} \\over {{K_1} + {K_2}}}} \\right)$$"}, {"identifier": "B", "content": "$${{{\\varepsilon _0}A} \\over d}\\left( {{1 \\over 2} + {{{K_1}{K_2}} \\over {2({K_1} + {K_2})}}} \\right)$$"}, {"identifier": "C", "content": "... | ["A"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267299/exam_images/kjco6hbyvnoygbkl0hmx.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266420/exam_images/ewo4wgxwqxzo6rski54b.webp"><source media="(max-wid... | mcq | jee-main-2021-online-26th-august-evening-shift | 9,307 |
1l547ofns | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :</p> | [{"identifier": "A", "content": "increase by 50%"}, {"identifier": "B", "content": "decrease by 15%"}, {"identifier": "C", "content": "increase by 25%"}, {"identifier": "D", "content": "increase by 33%"}] | ["A"] | null | <p>$$U = {1 \over 2}(k{C_0}){V^2}$$</p>
<p>$$ \Rightarrow {{U'} \over U} = 1.5$$</p>
<p>$$\Rightarrow$$ Energy increases by 50%</p> | mcq | jee-main-2022-online-29th-june-morning-shift | 9,309 |
1l58hr0iv | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :</p>
<p><img src="data:image/png;base64,UklGRn... | [{"identifier": "A", "content": "2$$\\mu$$F"}, {"identifier": "B", "content": "32$$\\mu$$F"}, {"identifier": "C", "content": "6$$\\mu$$F"}, {"identifier": "D", "content": "8$$\\mu$$F"}] | ["C"] | null | <p>Equivalent circuit is</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6s9x0na/535d80a1-e0af-4305-9424-ecd0df17bea2/a4c75260-1b3b-11ed-91de-637bbeffe542/file-1l6s9x0nb.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6s9x0na/535d80a1-e0af-4305-9424-ecd0df17bea2/a4c7526... | mcq | jee-main-2022-online-26th-june-evening-shift | 9,310 |
1l59maqgz | physics | capacitor | capacitors-with-dielectric | <p>Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness $${d \over 2}$$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?</p> | [{"identifier": "A", "content": "2 : 1"}, {"identifier": "B", "content": "1 : 2"}, {"identifier": "C", "content": "1 : 4"}, {"identifier": "D", "content": "4 : 1"}] | ["A"] | null | <p>$${C_{eq}} = {{{\varepsilon _0}A} \over {d - {d \over 2} + {d \over {2k}}}} = {{{\varepsilon _0}A} \over {{d \over 2}}} = {{2{\varepsilon _0}A} \over d}$$</p>
<p>If $$C = {{{\varepsilon _0}A} \over d}$$</p>
<p>$$ \Rightarrow {C_{eq}} = 2C$$ or $${{{C_{new}}} \over {{C_{old}}}} = {2 \over 1}$$</p> | mcq | jee-main-2022-online-25th-june-evening-shift | 9,311 |
1l6koe6ga | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor with width $$4 \mathrm{~cm}$$, length $$8 \mathrm{~cm}$$ and separation between the plates of $$4 \mathrm{~mm}$$ is connected to a battery of $$20 \mathrm{~V}$$. A dielectric slab of dielectric constant 5 having length $$1 \mathrm{~cm}$$, width $$4 \mathrm{~cm}$$ and thickness $$4 \mathrm{... | [] | null | 240 | <p>$${d_1} = 4 \times {10^{ - 3}}$$</p>
<p>$${A_1} = 8 \times 4 \times {10^{ - 4}}\,{m^2}$$</p>
<p>$$V = 20\,V$$</p>
<p>$${d_2} = 4 \times {10^{ - 3}},$$</p>
<p>$${A_2} = 4 \times 1 \times {10^{ - 4}}\,{m^2}$$</p>
<p>$${C_{eq}} = {{({A_1} + 5{A_2} - {A_2}){\varepsilon _0}} \over d} = {{3(16) \times {{10}^{ - 4}}} \over... | integer | jee-main-2022-online-27th-july-evening-shift | 9,313 |
1l6ma2gc4 | physics | capacitor | capacitors-with-dielectric | <p>Two capacitors, each having capacitance $$40 \,\mu \mathrm{F}$$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $$\mathrm{K}$$ such that the equivalence capacitance of the system became $$24 \,\mu \mathrm{F}$$. The value of $$\mathrm{K}$$ wil... | [{"identifier": "A", "content": "1.5"}, {"identifier": "B", "content": "2.5"}, {"identifier": "C", "content": "1.2"}, {"identifier": "D", "content": "3"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6z6ite4/3a105f96-a760-4f30-8d6f-d7a5e79bc293/db0148c0-1f07-11ed-8ba4-19601952a51f/file-1l6z6ite5.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6z6ite4/3a105f96-a760-4f30-8d6f-d7a5e79bc293/db0148c0-1f07-11ed-8ba4-19601952a51f... | mcq | jee-main-2022-online-28th-july-morning-shift | 9,314 |
1l6nrkg0z | physics | capacitor | capacitors-with-dielectric | <p>A slab of dielectric constant $$\mathrm{K}$$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $$\frac{3}{4} \mathrm{~d}$$, where $$\mathrm{d}$$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :</p>
<p>(G... | [{"identifier": "A", "content": "$$\\frac{4 K C_{0}}{3+K}$$"}, {"identifier": "B", "content": "$$\\frac{3 K C_{0}}{3+K}$$"}, {"identifier": "C", "content": "$$\\frac{3+K}{4 K C_{0}}$$"}, {"identifier": "D", "content": "$$\\frac{K}{4+K}$$"}] | ["A"] | null | <p>$${C_0} = {{{\varepsilon _0}A} \over d}$$</p>
<p>$$C = {{{\varepsilon _0}A} \over {d - {{3d} \over 4} + {{3d} \over {4K}}}} = {{4{\varepsilon _0}AK} \over {3d + Kd}}$$</p>
<p>$$ = {{4K{C_0}} \over {3 + K}}$$</p> | mcq | jee-main-2022-online-28th-july-evening-shift | 9,315 |
1ldtzqz7i | physics | capacitor | capacitors-with-dielectric | <p>A capacitor has capacitance 5$$\mu$$F when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $$\frac{d}{2}$$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ____... | [] | null | 6 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1ledm9s54/971e9f03-de7f-4bb1-892a-71705e3b5fb2/ee915380-b18d-11ed-a682-13f364283dca/file-1ledm9s55.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1ledm9s54/971e9f03-de7f-4bb1-892a-71705e3b5fb2/ee915380-b18d-11ed-a682-13f364283dca... | integer | jee-main-2023-online-25th-january-evening-shift | 9,316 |
1ldugmb5c | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor has plate area 40 cm$$^2$$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :</p> | [{"identifier": "A", "content": "$$\\mathrm{10\\varepsilon_0~F}$$"}, {"identifier": "B", "content": "$$\\mathrm{24\\varepsilon_0~F}$$"}, {"identifier": "C", "content": "$$\\mathrm{\\frac{3}{10}\\varepsilon_0~F}$$"}, {"identifier": "D", "content": "$$\\mathrm{\\frac{10}{3}\\varepsilon_0~F}$$"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le5k7nwf/9d447182-d3e9-4a54-a3bf-bb97dcd4e0ce/9c3824f0-ad1f-11ed-8bc1-d3bd0941e5b5/file-1le5k7nwg.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le5k7nwf/9d447182-d3e9-4a54-a3bf-bb97dcd4e0ce/9c3824f0-ad1f-11ed-8bc1-d3bd0941e5b5... | mcq | jee-main-2023-online-25th-january-morning-shift | 9,317 |
1ldws56c5 | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $$\frac{x}{4}$$ pF. The value of $$x$$ is ____________.</p> | [] | null | 105 | <p>Initially</p>
<p>$$
\frac{\varepsilon_{0} A}{d}=15 \times 10^{-12} \mathrm{~F}
$$</p>
<p>Finally</p>
$$
\begin{aligned}
& \frac{3.5 \varepsilon_{0} A}{2 d}=\frac{x}{4} \times 10^{-12} \mathrm{~F} \\\\
& \therefore \frac{3.5}{2} \times 15=\frac{x}{4} \\\\
& \Rightarrow x=\frac{3.5 \times 15 \times 4}{2}=105
\end{a... | integer | jee-main-2023-online-24th-january-evening-shift | 9,318 |
1lgvs3ne8 | physics | capacitor | capacitors-with-dielectric | <p>The distance between two plates of a capacitor is $$\mathrm{d}$$ and its capacitance is $$\mathrm{C}_{1}$$, when air is the medium between the plates. If a metal sheet of thickness $$\frac{2 d}{3}$$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $$\mathrm{C}_... | [{"identifier": "A", "content": "1 : 1"}, {"identifier": "B", "content": "3 : 1"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "4 : 1"}] | ["B"] | null | <p>When a metal sheet of thickness ($\frac{2d}{3}$) is introduced between the plates of a capacitor, it divides the capacitor into two separate capacitors. The metal sheet acts as a new plate in each capacitor, and because the metal is a conductor, it is at the same potential as the plates on either side. </p>
<p>The c... | mcq | jee-main-2023-online-10th-april-evening-shift | 9,319 |
1lh26bx37 | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor with plate area $$\mathrm{A}$$ and plate separation $$\mathrm{d}$$ is filled with a dielectric material of dielectric constant $$K=4$$. The thickness of the dielectric material is $$x$$, where $$x < d$$.</p>
<p><img src="data:image/png;base64,UklGRhIMAABXRUJQVlA4IAYMAACwmQCdASoAA/YAP4G6... | [] | null | 3 | Given,
$$
C_1=2 \mu \mathrm{F} \text { and } K=4
$$
<br/><br/>$\Rightarrow C_1=\frac{\varepsilon_0 A}{\left(\frac{\frac{d}{3}}{K}+\frac{2 d}{3}\right)}=\frac{\varepsilon_0 A}{\left(\frac{d}{3 \times 4}+\frac{2 d}{3}\right)}$
<br/><br/>$$
\Rightarrow 2 \mu F=\frac{\varepsilon_0 A \times 12}{9 d}=\frac{4}{3} \frac{\varep... | integer | jee-main-2023-online-6th-april-morning-shift | 9,320 |
lv2erj61 | physics | capacitor | capacitors-with-dielectric | <p>A parallel plate capacitor of capacitance $$12.5 \mathrm{~pF}$$ is charged by a battery connected between its plates to potential difference of $$12.0 \mathrm{~V}$$. The battery is now disconnected and a dielectric slab $$(\epsilon_{\mathrm{r}}=6)$$ is inserted between the plates. The change in its potential energy ... | [] | null | 750 | <p>$$\begin{aligned}
E_1 & =\frac{1}{2}\left(\frac{25}{2}\right) \times 10^{-12} \times 144 \\
& =900 \times 10^{-12} \mathrm{~J} \\
E_2 & =\frac{1}{2}\left(6 \times \frac{25}{2} \times 10^{-12}\right)\left(\frac{12}{6}\right)^2=150 \times 10^{-12} \mathrm{~J} \\
\Delta E & =750 \times 10^{-12} \mathrm{~J}
\end{aligned... | integer | jee-main-2024-online-4th-april-evening-shift | 9,322 |
lv3veewk | physics | capacitor | capacitors-with-dielectric | <p>A capacitor has air as dielectric medium and two conducting plates of area $$12 \mathrm{~cm}^2$$ and they are $$0.6 \mathrm{~cm}$$ apart. When a slab of dielectric having area $$12 \mathrm{~cm}^2$$ and $$0.6 \mathrm{~cm}$$ thickness is inserted between the plates, one of the conducting plates has to be moved by $$0.... | [{"identifier": "A", "content": "1.50"}, {"identifier": "B", "content": "0.66"}, {"identifier": "C", "content": "1.33"}, {"identifier": "D", "content": "1"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lw4xr87f/2bfc35fc-cdad-4ec5-bc19-fb1602f5ce82/af20e1b0-1123-11ef-a3e8-ff0446908720/file-1lw4xr87g.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lw4xr87f/2bfc35fc-cdad-4ec5-bc19-fb1602f5ce82/af20e1b0-1123-11ef-a3e8-ff0446908720... | mcq | jee-main-2024-online-8th-april-evening-shift | 9,323 |
lvb2acle | physics | capacitor | capacitors-with-dielectric | <p>A capacitor of $$10 \mu \mathrm{F}$$ capacitance whose plates are separated by $$10 \mathrm{~mm}$$ through air and each plate has area $$4 \mathrm{~cm}^2$$ is now filled equally with two dielectric media of $$K_1=2, K_2=3$$ respectively as shown in figure. If new force between the plates is $$8 \mathrm{~N}$$. The su... | [] | null | 80 | <p>$$\begin{array}{ll}
C_1=10 \mu \mathrm{F} & C_2=15 \mu \mathrm{F} \\
F=F_1+F_2 &
\end{array}$$</p>
<p>$$\begin{aligned}
& F=\frac{\left(10 \times 10^{-6} V\right)^2}{2 \cdot \frac{A}{2} \cdot \epsilon_0}+\frac{(15~~10)}{2 \cdot \frac{A}{2} \cdot \epsilon_0}=8 \\
& V^2=0.9 \times 10^{-4} \\
& V=0.95 \times 10^{-2} \m... | integer | jee-main-2024-online-6th-april-evening-shift | 9,324 |
iKPC6fPZN6En8nK4 | physics | capacitor | combination-of-capacitors | A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $$'s'$$ and mass $$'m'.$$ If the temperature of the block is raised by $$'\Delta T',$$ the potential difference $$'v'$$ across the capacitance i... | [{"identifier": "A", "content": "$${{mCAT} \\over s}$$ "}, {"identifier": "B", "content": "$$\\sqrt {{{2mCAT} \\over s}} $$ "}, {"identifier": "C", "content": "$$\\sqrt {{{2msAT} \\over C}} $$ "}, {"identifier": "D", "content": "$${{ms\\Delta T} \\over C}$$ "}] | ["C"] | null | Applying conservation of energy,
<br><br>$${1 \over 2}C{V^2} = m.s\Delta T;\,\,\,$$
<br><br>$$V = \sqrt {{{2m.s.\Delta T} \over C}} $$ | mcq | aieee-2005 | 9,325 |
AbtgcF7VNunrO7sO | physics | capacitor | combination-of-capacitors | A parallel plate capacitor is made by stacking $$n$$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $$'C'$$ then the resultant capacitance is | [{"identifier": "A", "content": "$$\\left( {n + 1} \\right)C$$ "}, {"identifier": "B", "content": "$$\\left( {n - 1} \\right)C$$ "}, {"identifier": "C", "content": "$$nC$$ "}, {"identifier": "D", "content": "$$C$$ "}] | ["B"] | null | As $$n$$ plates are joined, it means $$(n-1)$$ capacitor joined in parallel.
<br><br>$$\therefore$$ resultant capacitance $$=(n-1)C$$ | mcq | aieee-2005 | 9,326 |
b26FDjxWYnZBwJ5B | physics | capacitor | combination-of-capacitors | Two capacitors $${C_1}$$ and $${C_2}$$ are charged to $$120$$ $$V$$ and $$200$$ $$V$$ respectively. It is found that connecting them together the potential on each one can be made zero. Then | [{"identifier": "A", "content": "$$5{C_1} = 3{C_2}$$ "}, {"identifier": "B", "content": "$$3{C_1} = 5{C_2}$$ "}, {"identifier": "C", "content": "$$3{C_1} + 5{C_2} = 0$$ "}, {"identifier": "D", "content": "$$9{C_1} = 4{C_2}$$ "}] | ["B"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/3hjN6VPUKrhF8wmJe/9nSSVr34CsR1q8aQVzIsZy6bxcbnx/gCgSrRrj2yv32OSaUAlwzw/image.svg" loading="lazy" alt="JEE Main 2013 (Offline) Physics - Capacitor Question 132 English Explanation">
<br><br>For potential to be made zero, after connection
<br><br>$$120{C_1}... | mcq | jee-main-2013-offline | 9,327 |
m46LAUbOqynP20ys935wA | physics | capacitor | combination-of-capacitors | Three capacitors each of 4 $$\mu $$F are to be connected in such a way that the effective capacitance is 6 $$\mu $$F. This can be done by connecting them : | [{"identifier": "A", "content": "all in series"}, {"identifier": "B", "content": "two in series and one in parallel\n"}, {"identifier": "C", "content": "all in parallel"}, {"identifier": "D", "content": "two in parallel and one in series"}] | ["B"] | null | (a) $${1 \over {{C_{eq}}}} = {1 \over 4} + {1 \over 4} + {1 \over 4} = {3 \over 4}$$
<br><br>$$ \Rightarrow $$ $${C_{eq}} = {4 \over 3}\,\mu F$$
<br><br>(b) $${C_{eq}} = {{4 \times 4} \over {4 + 4}} + 4 = 6\mu F$$
<br><br>(c) $${C_{eq}} = 4 + 4 + 4 = 1... | mcq | jee-main-2016-online-9th-april-morning-slot | 9,328 |
Vm5EhImoQMZ6HIwzVqL6Q | physics | capacitor | combination-of-capacitors | Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $$\mu $$F is :
<br/><br/><img src="data:image/png;base64,UklGRn4IAABXRUJQVlA4IHIIAAAQjwCdASoAA6cBP4HA2mW2ML+nILLJm/AwCWlu4W+zMmNwvV6WtR... | [{"identifier": "A", "content": "$${{31} \\over {23}}\\,\\mu F$$"}, {"identifier": "B", "content": "$${{32} \\over {23}}\\,\\mu F$$"}, {"identifier": "C", "content": "$${{33} \\over {23}}\\,\\mu F$$"}, {"identifier": "D", "content": "$${{34} \\over {23}}\\,\\mu F$$"}] | ["B"] | null | Equivalent capacitance of 6 $$\mu $$F and 12 $$\mu $$F is = $${{6 \times 12} \over {12 + 6}}$$ = 4 $$\mu $$F
<br><br>Equivalent capacitance of 4$$\mu $$F and 4$$\mu $$F
<br><br>is = 4 + 4 = 8 $$\mu $$F
<br><br>New circuit is $$ \to $$
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l82xfh4a/b16... | mcq | jee-main-2016-online-10th-april-morning-slot | 9,329 |
TvcOamfSYKztPqXGalZY4 | physics | capacitor | combination-of-capacitors | The equivalent capacitance between $$A$$ and $$B$$ in the circuit given below, is :
<br/><br/><img src="data:image/png;base64,UklGRv4IAABXRUJQVlA4IPIIAABQewCdASoAAxwBP4HA2WS2MSynIXMqEsAwCWlu4WqH++uqPf7NWl8ddfPea1CEdqm5wgJR1Xqf+n2qXQlYOXUyoZCAizBLSO+ZN7VLoSYI2VQyEBKjkF9XIsXcy/g3lm03rmIGPyCYLHTRBC/+QW+MhASo4+qyBCOCq67O27... | [{"identifier": "A", "content": "$$2.4\\,\\mu F$$ "}, {"identifier": "B", "content": "$$4.9\\,\\mu F$$"}, {"identifier": "C", "content": "$$3.6\\,\\mu F$$"}, {"identifier": "D", "content": "$$5.4\\,\\mu F$$"}] | ["A"] | null | Given circuit :
<br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7u75irn/aeaa95d6-f29d-43c2-a485-43ad48018010/9e8a4930-3016-11ed-ab58-4f43f7f8c851/file-1l7u75iro.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7u75irn/aeaa95d6-f29d-43c2-a485-43ad48018010/9e8a4930-3016-11ed... | mcq | jee-main-2018-online-15th-april-morning-slot | 9,330 |
r3tKHDyhX7LYulegGIiDD | physics | capacitor | combination-of-capacitors | Seven capacitors, each of capacitance 2 $$\mu $$F, are to be connected in a configuration to obtain an effective capacitance of $$\left( {{6 \over {13}}} \right)\mu F.$$ Which of the combinations, shown in figures below, will achieve the desired value
| [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263409/exam_images/zyt785cqm1szxiahbjzp.webp\" style=\"max-width: 100%; height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2019 (Online) 11th January Evening Slot Physics - Capacitor Question 1... | ["A"] | null | C<sub>eq</sub> = $${6 \over {13}}$$$$\mu $$F
<br><br>Therefore three capacitors most be in parallel to get 6 in
<br><br>$${1 \over {{C_{eq}}}} = {1 \over {3C}} + {1 \over C} + {1 \over C} + {1 \over C} + {1 \over C}$$
<br><br>C<sub>eq</sub> = $${{3C} \over {13}}$$ = $${6 \over {13}}$$$$\mu $$F
<br><br><img src="https:... | mcq | jee-main-2019-online-11th-january-evening-slot | 9,331 |
zSymJsTJaagWLA6lrL18hoxe66ijvwwi4p7 | physics | capacitor | combination-of-capacitors | Figure shows charge (q) versus voltage (V)
graph for series and parallel combination of two
given capacitors. The capacitances are :
<img src="data:image/png;base64,UklGRlQQAABXRUJQVlA4IEgQAACQWwCdASptAQ0BPm00l0ikIqIhI7EZeIANiWlu/HyYacuelXRkpD+FP4z+K/ft/Rfx5/eD2P/D/mv7B+RP5Pe9hWk/1/8U81X1B+z/x7+k/57+v/u17wf2b8ov6B6W/Ar... | [{"identifier": "A", "content": "40 $$\\mu $$F and 10 $$\\mu $$F"}, {"identifier": "B", "content": "60 $$\\mu $$F and 40 $$\\mu $$F"}, {"identifier": "C", "content": "20 $$\\mu $$F and 30 $$\\mu $$F"}, {"identifier": "D", "content": "50 $$\\mu $$F and 30 $$\\mu $$F"}] | ["A"] | null | As q = CV<br>
Hence slope of graph will give capacitance. Slope will be more in parallel combination.
Hence capacitance in parallel should be 50 $$\mu $$F and in series combination must be 8 $$\mu $$F.
Only in option 40 $$\mu $$f and 10 $$\mu $$F.<br><br>
C<sub>parallel</sub> = 40 + 10 = 50 $$\mu $$F<br><br>
C<sub>seri... | mcq | jee-main-2019-online-10th-april-morning-slot | 9,333 |
TOEYT0qdXMT1XVm1IV7k9k2k5feant1 | physics | capacitor | combination-of-capacitors | A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and
is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost
in this process by the time the charge is redistributed between them is (in nJ) _____ | [] | null | 6 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265616/exam_images/se6f7getrznbywz5wib4.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 7th January Evening Slot Physics - Capacitor Question 95 English Explanation">
<br>U<sub>i</sub> =... | integer | jee-main-2020-online-7th-january-evening-slot | 9,334 |
sOnP4Jn4DRemgv4oqt7k9k2k5gy26s4 | physics | capacitor | combination-of-capacitors | Effective capacitance of parallel combination
of two capacitors C<sub>1</sub> and C<sub>2</sub> is 10 μF. When
these capacitors are individually connected to
a voltage source of 1V, the energy stored in the
capacitor C<sub>2</sub> is 4 times that of C<sub>1</sub>. If these
capacitors are connected in series, their
effe... | [{"identifier": "A", "content": "4.2 \u03bcF"}, {"identifier": "B", "content": "8.4 \u03bcF"}, {"identifier": "C", "content": "1.6 \u03bcF"}, {"identifier": "D", "content": "3.2 \u03bcF"}] | ["C"] | null | C<sub>1</sub>
+ C<sub>2</sub>
= 10 ......(1)
<br><br>$${1 \over 2}{C_2}{V^2} = 4 \times {1 \over 2}{C_1}{V^2}$$
<br><br>$$ \Rightarrow $$ C<sub>2</sub>
= 4C<sub>1</sub> .....(2)
<br><br>From (1) ans (2),
<br><br>C<sub>1</sub>
= 2 and C<sub>2</sub>
= 8
<br><br>For series combination
<br><br>C<sub>eq</sub> = $${{{C... | mcq | jee-main-2020-online-8th-january-morning-slot | 9,335 |
kTuGSfbhwGMLqOtALhjgy2xukff4pjif | physics | capacitor | combination-of-capacitors | Two capacitors of capacitances C and 2C are
charged to potential differences V and 2V,
respectively. These are then connected in
parallel in such a manner that the positive
terminal of one is connected to the negative
terminal of the other. The final energy of this
configuration is : | [{"identifier": "A", "content": "Zero"}, {"identifier": "B", "content": "$${3 \\over 2}C{V^2}$$"}, {"identifier": "C", "content": "$${9 \\over 2}C{V^2}$$"}, {"identifier": "D", "content": "$${{25} \\over 6}C{V^2}$$"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266447/exam_images/vbuasjqxftln1akirgfi.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 5th September Morning Slot Physics - Capacitor Question 86 English Explanation">
<br><br>By conser... | mcq | jee-main-2020-online-5th-september-morning-slot | 9,336 |
usia2yeY7zUov0GDFR1klribci5 | physics | capacitor | combination-of-capacitors | Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be : | [{"identifier": "A", "content": "4 : 1"}, {"identifier": "B", "content": "1 : 2"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "1 : 4"}] | ["D"] | null | Given, C<sub>1</sub> = C<sub>2</sub> = C<br/><br/>When both capacitors are connected in series, their equivalent capacitance will be<br/><br/>$${1 \over {{C_s}}} = {1 \over C} + {1 \over C} = {2 \over C}$$<br/><br/>$$ \Rightarrow {C_s} = {C \over 2}$$<br/><br/>When both capacitors are connected in parallel, their equiv... | mcq | jee-main-2021-online-24th-february-morning-slot | 9,337 |
zJfSF6XvoLbexyqqhM1klth5e6m | physics | capacitor | combination-of-capacitors | Consider the combination of 2 capacitors C<sub>1</sub> and C<sub>2</sub> with C<sub>2</sub> > C<sub>1</sub>, when connected in parallel, the equivalent capacitance is $${{15} \over 4}$$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $${{{C_2}} \over {{C_1}}}$$. | [{"identifier": "A", "content": "$${{15} \\over {11}}$$"}, {"identifier": "B", "content": "No Solutions"}, {"identifier": "C", "content": "$${{29} \\over {15}}$$"}, {"identifier": "D", "content": "$${{15} \\over {4}}$$"}] | ["B"] | null | When connected in parallel<br><br>C<sub>eq</sub> = C<sub>1</sub> + C<sub>2</sub><br><br>When in series<br><br>$$C{'_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}$$<br><br>$${C_1} + {C_2} = {{15} \over 4}\left( {{{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)$$<br><br>$$4{({C_1} + {C_2})^2} = 15{C_1}{C_2}$$<br><br>$$4{C_1}... | mcq | jee-main-2021-online-26th-february-morning-slot | 9,338 |
9gwONG3q1emhe2FEeg1kmj44n72 | physics | capacitor | combination-of-capacitors | Four identical rectangular plates with length, l = 2 cm and breadth, b = $${3 \over 2}$$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $${{x{\varepsilon _0}} \over d}$$. The value of x is ______________. (Round off to the Nearest Integer)<br/><br/><img src="data:image/png;base64,UklG... | [] | null | 2 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266426/exam_images/drhywx1eqad0amlc9olf.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Morning Shift Physics - Capacitor Question 76 English Explanation">
<br>$${C_{eq}} = {{... | integer | jee-main-2021-online-17th-march-morning-shift | 9,339 |
1l56w796n | physics | capacitor | combination-of-capacitors | <p>A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $${x \over {15}}{{{ \in _0}A} \over b}$$. The value of x is ____________.</p>
<p> <img src="data:image/png;base6... | [] | null | 23 | <p>The circuit is equivalent to 3 capacitors in parallel as shown</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5ifp0jv/ee20bc3a-b2ec-4046-ba72-532a22c1378c/2f224db0-0206-11ed-aa88-69f11483e075/file-1l5ifp0jw.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5ifp0jv/ee2... | integer | jee-main-2022-online-27th-june-evening-shift | 9,340 |
1l6gmpfsx | physics | capacitor | combination-of-capacitors | <p>The total charge on the system of capacitors $$C_{1}=1 \mu \mathrm{F}, C_{2}=2 \mu \mathrm{F}, \mathrm{C}_{3}=4 \mu \mathrm{F}$$ and $$\mathrm{C}_{4}=3 \mu \mathrm{F}$$ connected in parallel is :</p>
<p>(Assume a battery of $$20 \mathrm{~V}$$ is connected to the combination)</p> | [{"identifier": "A", "content": "$$200 \\,\\mu \\mathrm{C}$$"}, {"identifier": "B", "content": "200 C"}, {"identifier": "C", "content": "$$10 \\,\\mu \\mathrm{C}$$"}, {"identifier": "D", "content": "10 C"}] | ["A"] | null | <p>Equivalent $$C = \sum {{C_i}} $$</p>
<p>$$ = 10\,\mu F$$</p>
<p>$$\Rightarrow$$ Charge $$Q = CV$$</p>
<p>$$ = 200\,\mu C$$</p> | mcq | jee-main-2022-online-26th-july-morning-shift | 9,342 |
1lgxww9p2 | physics | capacitor | combination-of-capacitors | <p>The equivalent capacitance of the combination shown is :</p>
<p><img src="data:image/png;base64,UklGRmwFAABXRUJQVlA4IGAFAACQYgCdASoAAxQBP4G+2WO2MKwmpxEYWsAwCWlu+F6oJK5JNlvj6VfeS7LR1DkRcKVBBSBqazfCZ6nV20pUXx9ERcKVF8fREUyqDLRBD8FzafMfoiLhSovj6Ii4UqL4+iItxf5uT/7dl5ecx52bV332oLRR3EJ+TLLy8nED+rcJaDWuy8vJxM2W0Y88QrhLQUaS/... | [{"identifier": "A", "content": "$$\\frac{C}{2}$$"}, {"identifier": "B", "content": "4C"}, {"identifier": "C", "content": "$$\\frac{5}{3}$$C"}, {"identifier": "D", "content": "2C"}] | ["D"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1loi546u3/49da847f-7623-4cd3-aeab-4cb507354411/ece766b0-7a04-11ee-bbdd-cfc3c972af88/file-6y3zli1loi546u4.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1loi546u3/49da847f-7623-4cd3-aeab-4cb507354411/ece766b0-7a04-11ee-bb... | mcq | jee-main-2023-online-10th-april-morning-shift | 9,343 |
1lh30zi2t | physics | capacitor | combination-of-capacitors | <p>As shown in the figure, two parallel plate capacitors having equal plate area of $$200 \mathrm{~cm}^{2}$$ are joined in such a way that $$a \neq b$$. The equivalent capacitance of the combination is $$x \in_{0} \mathrm{~F}$$. The value of $$x$$ is ____________.</p>
<p><img src="data:image/png;base64,UklGRnoIAABXRUJQ... | [] | null | 5 | $$
\begin{aligned}
& c=\frac{\varepsilon_0 A}{(d-c)} \\\\
& =\frac{\varepsilon_0 \times 200 \times 10^{-4}}{4 \times 10^{-3}} \\\\
& \therefore x=5
\end{aligned}
$$<br/><br/>
The situation is equivalent to a conducting slab placed between the plates | integer | jee-main-2023-online-6th-april-evening-shift | 9,344 |
lsamif14 | physics | capacitor | combination-of-capacitors | A galvanometer $(G)$ of $2 \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is :
<img src="data:image/png;base64,UklGRnAUAABXRUJQVlA4IGQUAACQNgGdASpyAgADP4HA2GS2MCynIhY52sAwCWlu+/iW0lJNCB4T7fy3/af8L1m3W7A+vKywrj/aX+28bTCHV/9EenF9mfxH/96ojgmMPy6Mpph+NLUgdkZSa7miaNY+OPDh... | [{"identifier": "A", "content": "1"}, {"identifier": "B", "content": "$\\frac{2}{3}$"}, {"identifier": "C", "content": "$\\frac{3}{2}$"}, {"identifier": "D", "content": "$\\frac{1}{2}$"}] | ["D"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsc4gqim/e6fad96e-f70e-4ec2-8529-57b14590ac2d/8a4e95e0-c5e6-11ee-9fee-3bdb52bb2fc8/file-6y3zli1lsc4gqin.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsc4gqim/e6fad96e-f70e-4ec2-8529-57b14590ac2d/8a4e95e0-c5e6-11ee-9f... | mcq | jee-main-2024-online-1st-february-evening-shift | 9,345 |
jaoe38c1lsfm5bi3 | physics | capacitor | combination-of-capacitors | <p>In the given figure, the charge stored in $$6 \mu F$$ capacitor, when points $$A$$ and $$B$$ are joined by a connecting wire is __________ $$\mu C$$.</p>
<p><img src="data:image/png;base64,UklGRtgKAABXRUJQVlA4IMwKAAAwrgCdASodAgADP4G+2WY2LyynIPIpIsAwCWlu4W+zlmNwvj5q/3lsDZydo8x+II2/+P6F6uLVcNM+GNwvecLxEAPFHGj0PSpiISDp... | [] | null | 36 | <p>At steady state, capacitor behaves as an open circuit and current flows in circuit as shown in the diagram.</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsr7n3ip/11a2b1a8-833e-4741-bb7a-c2bdd9147314/b855c720-ce32-11ee-9412-cd4f9c6f2c40/file-6y3zli1lsr7n3iq.png?format=png" data-orsrc=... | integer | jee-main-2024-online-29th-january-evening-shift | 9,346 |
1lsgxeosz | physics | capacitor | combination-of-capacitors | <p>A capacitor of capacitance $$\mathrm{C}$$ and potential $$\mathrm{V}$$ has energy $$\mathrm{E}$$. It is connected to another capacitor of capacitance $$2 \mathrm{C}$$ and potential $$2 \mathrm{~V}$$. Then the loss of energy is $$\frac{x}{3} \mathrm{E}$$, where $$x$$ is _______.</p> | [] | null | 2 | <p>$$\begin{aligned}
& \text { Energy loss }=\frac{1}{2} \frac{C_1 C_2}{C_1+C_2}\left(V_1-V_2\right)^2 \\
& =\frac{2}{3} \cdot E \\
& \therefore x=2
\end{aligned}$$</p> | integer | jee-main-2024-online-30th-january-morning-shift | 9,347 |
lv7v3twm | physics | capacitor | combination-of-capacitors | <p>Three capacitors of capacitances $$25 \mu \mathrm{F}, 30 \mu \mathrm{F}$$ and $$45 \mu \mathrm{F}$$ are connected in parallel to a supply of $$100 \mathrm{~V}$$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $$\frac{9}{x} \mathrm{E... | [] | null | 86 | <p>$$E=\frac{1}{2}(25+30+45)(100)^2 \quad \text{.... (i)}$$</p>
<p>$$\text { Also, } \frac{9}{x} E=\frac{1}{2} \frac{1}{\left(\frac{1}{25}+\frac{1}{30}+\frac{1}{45}\right)}(100)^2 \quad \text{.... (ii)}$$</p>
<p>From (i) and (ii)</p>
<p>$$x=86$$</p> | integer | jee-main-2024-online-5th-april-morning-shift | 9,348 |
ATq5YUf6zKjfi4zD | physics | capacitor | electric-energy-stored-by-capacitor | The work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity $$100$$ micro-farad is | [{"identifier": "A", "content": "$$16 \\times {10^{ - 32}}\\,\\,joule$$ "}, {"identifier": "B", "content": "$$3.1 \\times {10^{ - 26}}\\,\\,joule$$"}, {"identifier": "C", "content": "$$4 \\times {10^{ - 10}}\\,\\,joule$$"}, {"identifier": "D", "content": "$$32 \\times {10^{ - 32}}\\,\\,joule$$"}] | ["D"] | null | The work done is stored as the potential energy. The potential energy stored in a capacitor is given by
<br><br>$$U = {1 \over 2}{{{Q^2}} \over C}$$
<br><br>$$ = {1 \over 2} \times {{{{\left( {8 \times {{10}^{ - 18}}} \right)}^2}} \over {100 \times {{10}^{ - 6}}}}$$
<br><br>$$ = 32 \times {10^{ - 32}}J$$ | mcq | aieee-2003 | 9,350 |
4gKcYdKAcylRDCPo | physics | capacitor | electric-energy-stored-by-capacitor | A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be | [{"identifier": "A", "content": "$$1/2$$ "}, {"identifier": "B", "content": "$$1$$ "}, {"identifier": "C", "content": "$$2$$ "}, {"identifier": "D", "content": "$$1/4$$ "}] | ["A"] | null | Required ratio
<br><br>$$ = {{Energy\,\,\,stored\,\,in\,\,capacitor} \over {Workdone\,\,by\,\,the\,\,battery}} = {{{1 \over 2}C{V^2}} \over {C{e^2}}}$$
<br><br>where $$C=$$ Capacitance of capacitor
<br><br>$$V=$$ Potential difference,
<br><br>$$e=$$ $$emf$$ of battery
<br><br>$$ = {{{1 \over 2}C{e^2}} \over {C{e^2}}} ... | mcq | aieee-2007 | 9,351 |
IR7UpTJU5ifGk8SbKs0WT | physics | capacitor | electric-energy-stored-by-capacitor | The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu $$C charge, its radius will be :
<br/>[ Take : $${1 \over {4\,\pi { \in _0}}} = $$ 9 $$ \times $$ 10<sup>9</sup> N $$-$$ m<sup>2</sup>/C<sup>2</sup> ] | [{"identifier": "A", "content": "20 mm"}, {"identifier": "B", "content": "32 mm"}, {"identifier": "C", "content": "28 mm"}, {"identifier": "D", "content": "16 mm"}] | ["D"] | null | Energy of sphere = $${{{Q^2}} \over {2C}}$$
<br><br>$$\therefore\,\,\,$$ $${{16 \times {{10}^{ - 12}}} \over {2C}}$$ = 4.5
<br><br>$$ \Rightarrow $$$$\,\,\,$$ C = $${{16 \times {{10}^{ - 12}}} \over 9}$$
<br><br>We know capacity of spherical conductor,
<br><br>C = 4$$\pi $$$$\varepsilon $$<sub>0</sub>R
<br><br>$$\the... | mcq | jee-main-2017-online-8th-april-morning-slot | 9,352 |
cj8kuYoLnyBRwJZPzYS3u | physics | capacitor | electric-energy-stored-by-capacitor | A capacitor with capacitance 5μF is charged to
5μC. If the plates are pulled apart to reduce the
capacitance to 2μF, how much work is done ? | [{"identifier": "A", "content": "2.16 \u00d7 10<sup>\u20136</sup> J"}, {"identifier": "B", "content": "2.55 \u00d7 10<sup>\u20136</sup> J"}, {"identifier": "C", "content": "3.75 \u00d7 10<sup>\u20136</sup> J"}, {"identifier": "D", "content": "6.25 \u00d7 10<sup>\u20136</sup> J"}] | ["C"] | null | Work done = $$\Delta $$U<br><br>
= U<sub>f</sub> – U<sub>i</sub><br><br>
$$ = {{{q^2}} \over {2{C_r}}} - {{{q^2}} \over {2{C_i}}}$$<br><br>
$$ = {{{{\left( {5 \times {{10}^{ - 6}}} \right)}^2}} \over 2}.\left( {{1 \over {2 \times {{10}^{ - 6}}}} - {1 \over {5 \times {{10}^{ - 6}}}}} \right)$$<br><br>
$$ = {{15} \over 4... | mcq | jee-main-2019-online-9th-april-morning-slot | 9,353 |
diJPB66bx97pr0xEkxjgy2xukev4tlaz | physics | capacitor | electric-energy-stored-by-capacitor | A 5 $$\mu $$F capacitor is charged fully by a 220 V
supply. It is then disconnected from the supply
and is connected in series to another
uncharged 2.5 $$\mu $$F capacitor. If the energy
change during the charge redistribution is
$${X \over {100}}J$$ then value of X to the nearest integer is
_____. | [] | null | 4 | u<sub>i</sub> = $$\frac{1}{2} $$ $$ \times $$ 5 $$ \times $$ 10<sup>-6</sup>$$ \times $$220
<br><br>Final common potential
<br><br>= $$\frac{220\times 5+0\times 2.5}{5+2.5} $$ = 220 $$ \times $$ $$\frac{2}{3} $$
<br><br>u<sub>f</sub> = $$\frac{1}{2} $$ $$ \times $$ (5 + 2.5)$$ \times $$10<sup>-6</sup> $$ \times $$ $$\l... | integer | jee-main-2020-online-2nd-september-morning-slot | 9,354 |
WZn2bepXulzyRgAsdAjgy2xukfakors2 | physics | capacitor | electric-energy-stored-by-capacitor | A capacitor C is fully charged with voltage V<sub>0</sub>. After disconnecting the voltage source, it is connected
in parallel with another uncharged capacitor of capacitance $${C \over 2}$$. The energy loss in the process
after the charge is distributed between the two capacitors is : | [{"identifier": "A", "content": "$${1 \\over 2}CV_0^2$$"}, {"identifier": "B", "content": "$${1 \\over 4}CV_0^2$$"}, {"identifier": "C", "content": "$${1 \\over 3}CV_0^2$$"}, {"identifier": "D", "content": "$${1 \\over 6}CV_0^2$$"}] | ["D"] | null | Heat loss = $${1 \over 2}\left( {{{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)V_0^2$$
<br><br>= $${1 \over 2}\left( {{{C \times {C \over 2}} \over {C + {C \over 2}}}} \right)V_0^2$$
<br><br>= $${1 \over 6}CV_0^2$$ | mcq | jee-main-2020-online-4th-september-evening-slot | 9,355 |
3VKTSW8cNgRjUyAhhB1kmj40voe | physics | capacitor | electric-energy-stored-by-capacitor | A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant... | [] | null | 864 | $${U_i} = {1 \over 2}c{v^2}$$<br><br>$$ = {1 \over 2} \times 14 \times {(12)^2}$$ pJ<br><br>= 1008 pJ<br><br>$${U_f} = {{{Q^2}} \over {2kC}}$$<br><br>$$ = {{{{(14 \times 12)}^2}} \over {2 \times 7 \times 14}}$$<br><br>= 144 pJ<br><br>oscillating energy = U<sub>i</sub> $$-$$ U<sub>f</sub><br><br>= 1008 $$-$$ 144<br><br>... | integer | jee-main-2021-online-17th-march-morning-shift | 9,356 |
1ldr39c2q | physics | capacitor | electric-energy-stored-by-capacitor | <p>A capacitor of capacitance $$900 \mu \mathrm{F}$$ is charged by a $$100 \mathrm{~V}$$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connecte... | [] | null | 225 | <p>$${U_i} = {1 \over 2}C{V^2} = {1 \over 2} \times 900 \times {10^{ - 6}} \times {100^2} = 4.5$$ J</p>
<p>As the other capacitor is identical therefore charge is equally divided and potential difference across the capacitors becomes half. So</p>
<p>$${U_f} = {1 \over 2}2C{\left( {{V \over 2}} \right)^2} = {1 \over 2} ... | integer | jee-main-2023-online-30th-january-morning-shift | 9,359 |
1lgyredx6 | physics | capacitor | electric-energy-stored-by-capacitor | <p>A $$600 ~\mathrm{pF}$$ capacitor is charged by $$200 \mathrm{~V}$$ supply. It is then disconnected from the supply and is connected to another uncharged $$600 ~\mathrm{pF}$$ capacitor. Electrostatic energy lost in the process is ____________ $$\mu \mathrm{J}$$</p> | [] | null | 6 | <p>The energy stored in a capacitor can be calculated using the formula:</p>
<p>$ U = \frac{1}{2} C V^2 $</p>
<p>where:</p>
<ul>
<li>(U) is the energy,</li>
<li>(C) is the capacitance,</li>
<li>(V) is the voltage.</li>
</ul>
<p>Initially, the energy stored in the first capacitor is:</p>
<p>$ U_{\text{initial}} = \frac{... | integer | jee-main-2023-online-8th-april-evening-shift | 9,361 |
lsbl4bgb | physics | capacitor | electric-energy-stored-by-capacitor | Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is : | [{"identifier": "A", "content": "$\\frac{1}{4} \\mathrm{CV}^2$"}, {"identifier": "B", "content": "$\\frac{3}{4} \\mathrm{CV}^2$"}, {"identifier": "C", "content": "$\\frac{1}{2} \\mathrm{CV}^2$"}, {"identifier": "D", "content": "$2 \\mathrm{CV}^2$"}] | ["A"] | null | <p>To solve the problem, let's start by considering the energy stored in each capacitor before they are connected together.
<p>The energy stored in a capacitor is given by the formula:</p></p>
<p>$$E = \frac{1}{2} C V^2$$</p>
<p>Where $E$ is the energy, $C$ is the capacitance, and $V$ is the potential.
<p>For the f... | mcq | jee-main-2024-online-1st-february-morning-shift | 9,362 |
jaoe38c1lsf29y5g | physics | capacitor | electric-energy-stored-by-capacitor | <p>A $$16 \Omega$$ wire is bend to form a square loop. A $$9 \mathrm{~V}$$ battery with internal resistance $$1 \Omega$$ is connected across one of its sides. If a $$4 \mu F$$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $$\frac{x}{2} \mu J$$, where $$x=$$ _________</p> | [] | null | 81 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lt2xedjy/60f44ef6-b510-41ec-ab7a-933525632e2d/124e23e0-d4a4-11ee-bdd1-01c80c3e2d9a/file-1lt2xedjz.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lt2xedjy/60f44ef6-b510-41ec-ab7a-933525632e2d/124e23e0-d4a4-11ee-bdd1-01c80c3e2d9a... | integer | jee-main-2024-online-29th-january-morning-shift | 9,363 |
e6AD5TmcSOt28q1g | physics | capacitor | parallel-plate-capacitor | A parallel plate condenser with a dielectric of dielectric constant $$K$$ between the plates has a capacity $$C$$ and is charged to a potential $$V$$ volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is | [{"identifier": "A", "content": "zero "}, {"identifier": "B", "content": "$${1 \\over 2}\\,\\left( {K - 1} \\right)\\,C{V^2}$$ "}, {"identifier": "C", "content": "$${{C{V^2}\\left( {K - 1} \\right)} \\over K}$$ "}, {"identifier": "D", "content": "$$\\left( {K - 1} \\right)\\,C{V^2}$$ "}] | ["A"] | null | <p>First, let's consider the capacitor with the dielectric between its plates. The charge on the capacitor is Q, its capacitance is C (which includes the effect of the dielectric), and the potential difference (voltage) across its plates is V. According to the formula for the energy stored in a capacitor :</p>
<p>$... | mcq | aieee-2007 | 9,364 |
gr7JyZIT9ApQgH5ZRtR2i | physics | capacitor | parallel-plate-capacitor | A parallel plate capacitor with area 200 cm<sup>2</sup> and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $$25 \times {10^{ - 6}}N,$$ the value of V is approximately : $$\left( {{ \in _o} = 8.85 \times {{10}^{ - 12}}{{{C^2}} \over {N.{m^2... | [{"identifier": "A", "content": "250 V"}, {"identifier": "B", "content": "100 V"}, {"identifier": "C", "content": "300 V"}, {"identifier": "D", "content": "150 V"}] | ["A"] | null | Given area of Parallel plate capacitor, A = 200 cm<sup>2</sup>
<br><br/>Separation between the plates, d = 1.5 cm
<br><br/>Force of attraction between the plates, F = 25 × 10<sup>–6</sup> N
<br><br>F = QE
<br><br>$$ \Rightarrow $$ F = $${{{Q^2}} \over {2A{ \in _0}}}$$
<br><br>[ As E due to parallel plate = $${\sigma \... | mcq | jee-main-2018-online-15th-april-evening-slot | 9,365 |
QR0yg1kEIJGexqv0gRpbT | physics | capacitor | parallel-plate-capacitor | A parallel plate capacitor with plates of area 1 m<sup>2</sup> each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :
<br/><br/>(Take $$\varepsilon $$<sub>0</sub> = 8.85 $$ \times $$ 10<sup>$$-$$12</sup> $${{{C^2}} \over {N - {m^2}}}$$) | [{"identifier": "A", "content": "9.85 $$ \\times $$ 10<sup>\u201310</sup> C"}, {"identifier": "B", "content": "8.85 $$ \\times $$ 10<sup>\u201310</sup> C"}, {"identifier": "C", "content": "6.85 $$ \\times $$ 10<sup>\u201310</sup> C"}, {"identifier": "D", "content": "7.85 \u00d7 10<sup>\u201310</sup> C"}] | ["B"] | null | $$E = {\sigma \over {{ \in _0}}} = {Q \over {A\,{ \in _0}}}$$
<br><br>Q = AE$$ \in $$<sub>0</sub>
<br><br>Q = (1) (100) (8.85 $$ \times $$ 10<sup>$$-$$12</sup>)
<br><br>Q = 8.85 $$ \times $$ 10<sup>$$-$$10</sup>C | mcq | jee-main-2019-online-12th-january-evening-slot | 9,366 |
q8jqIBO8zn1wh5ntAT3rsa0w2w9jwzlnauu | physics | capacitor | parallel-plate-capacitor | A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field
E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :
<img src="data:image/png;base64,UklGRnIKAABXRUJQVlA4IGYKAADQUwCdASpWAVEBPm02mkgkIyKhI1PZaIANiWlu4XJ17mNwsR... | [{"identifier": "A", "content": "$$2\\pi \\sqrt {{L \\over {\\sqrt {{g^2} - {{{q^2}{E^2}} \\over {{m^2}}}} }}} $$"}, {"identifier": "B", "content": "$$2\\pi \\sqrt {{L \\over {\\left( {g + {{qE} \\over m}} \\right)}}} $$"}, {"identifier": "C", "content": "$$2\\pi \\sqrt {{L \\over {\\sqrt {{g^2} + {{{q^2}{E^2}} \\over ... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266245/exam_images/oa0msgmeubb9vzqvpeyd.webp" style="max-width: 100%;max-height:250px;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 10th April Evening Slot Physics - Capacitor Question 99 English Explanation">
$$t... | mcq | jee-main-2019-online-10th-april-evening-slot | 9,368 |
1l57q90xt | physics | capacitor | parallel-plate-capacitor | <p>A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.</p> | [{"identifier": "A", "content": "5 N"}, {"identifier": "B", "content": "10 N"}, {"identifier": "C", "content": "20 N"}, {"identifier": "D", "content": "Zero"}] | ["A"] | null | <p>E between two plates is $${\sigma \over {{\varepsilon _0}}}$$ and due to one plate is $${\sigma \over {2{\varepsilon _0}}}$$ so the force will be halved</p>
<p>So new force F = 5 N</p> | mcq | jee-main-2022-online-27th-june-morning-shift | 9,370 |
1l6rgj5f7 | physics | capacitor | parallel-plate-capacitor | <p>Two identical thin metal plates has charge $$q_{1}$$ and $$q_{2}$$ respectively such that $$q_{1}>q_{2}$$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :</p> | [{"identifier": "A", "content": "$$\\frac{\\left(q_{1}+q_{2}\\right)}{C}$$"}, {"identifier": "B", "content": "$$\\frac{\\left(q_{1}-q_{2}\\right)}{C}$$"}, {"identifier": "C", "content": "$$\\frac{\\left(q_{1}-q_{2}\\right)}{2 C}$$"}, {"identifier": "D", "content": "$$\\frac{2\\left(q_{1}-q_{2}\\right)}{C}$$"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l79fmjbf/beef1ae2-10b1-4672-9c56-1efa220d1b8b/4b1d91b0-24ab-11ed-8d2e-5f0df5271c2d/file-1l79fmjbg.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l79fmjbf/beef1ae2-10b1-4672-9c56-1efa220d1b8b/4b1d91b0-24ab-11ed-8d2e-5f0df5271c2d... | mcq | jee-main-2022-online-29th-july-evening-shift | 9,372 |
ldo7ofph | physics | capacitor | parallel-plate-capacitor | Two parallel plate capacitors $C_{1}$ and $C_{2}$ each having capacitance of $10 \mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor $C_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $\mathrm{C}_{2}$ is disconnected from the source and then a d... | [] | null | 55 | Charge on $\mathrm{C}_{1}=\mathrm{KCV}$
<br/><br/>And charge on $\mathrm{C}_{2}=\mathrm{CV}$
<br/><br/>When they are connected in parallel charge will be equally divided so charge on one capacitor is
<br/><br/>$q=\frac{K+1}{2} \mathrm{CV}$
<br/><br/>So, $V=\frac{q}{K C}=\frac{K+1}{2 K}=55 \mathrm{~V}$ | integer | jee-main-2023-online-31st-january-evening-shift | 9,373 |
1lgswsttc | physics | capacitor | parallel-plate-capacitor | <p>A capacitor of capacitance $$\mathrm{C}$$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :</p> | [{"identifier": "A", "content": "Zero"}, {"identifier": "B", "content": "$$\\frac{C V}{\\varepsilon_{0}}$$"}, {"identifier": "C", "content": "$$\\frac{C V}{2 \\varepsilon_{0}}$$"}, {"identifier": "D", "content": "$$\\frac{2 C V}{\\varepsilon_{0}}$$"}] | ["B"] | null | <p>The electric field inside a parallel plate capacitor is uniform and given by $\mathbf{E}=\frac{V}{d} \hat{\mathbf{j}}$ where $d$ is the separation between the plates. <br/><br/>The electric flux through a closed surface enclosing only the positive plate of the capacitor is given by $\Phi_E = \oint_S \mathbf{E}\cdot ... | mcq | jee-main-2023-online-11th-april-evening-shift | 9,374 |
C9HGa3gABDwNQm4vob1qpqahkk8fhkhtw | physics | capacitor | rc-circuit | The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $$\tau $$ of this circuit lies between
<img src="data:image/png;base64,UklGRmwPAABXRUJQVlA4IGAPAADwggCdASr0AVcBP4G21WW2LKunITCqSsAwCWlu4WQC4mNwvV5i7R/Amvrty/2nerwAv3/bdwCd1PNc+o2Hc8b4K/3L/2esWLMn5JxRpJInOi9ElilAtk+... | [{"identifier": "A", "content": "100 sec and 150 sec"}, {"identifier": "B", "content": "0 and 50 sec"}, {"identifier": "C", "content": "50 sec and 100 sec"}, {"identifier": "D", "content": "150 sec and 200 sec "}] | ["A"] | null | During discharging of a capacitor, V = V<sub>0</sub>$${e^{ - {t \over \tau }}}$$
<br><br>At t = $$\tau $$,
<br><br>V = $${{{V_0}} \over e}$$ = 0.37V<sub>0</sub>
<br><br>From the graph, t = 0, V<sub>0</sub> = 25 V
<br><br>$$ \therefore $$ V = 0.37 $$ \times $$ 25 = 9.25 V
<br><br>This voltage will occur at time between ... | mcq | aieee-2012 | 9,376 |
vCQT6Zfy0CzhYiVu | physics | capacitor | rc-circuit | In the given circuit diagram when the current reaches steady state in the
circuit, the charge on the capacitor of capacitance C will be: <br/><br/>
<img src="data:image/png;base64,UklGRkwQAABXRUJQVlA4IEAQAAAQCAGdASoAA84CP4G61mY2LawpoRBJesAwCWlu4XHDgmNwvH6o/3n9j9o/TjzZ1fTuL3l///3/+Gvbn/BeIF+Mf9v1h33n0swrd/2UA85//+wf+iDt... | [{"identifier": "A", "content": "$$CE{{{r_1}} \\over {({r_1} + r)}}$$ "}, {"identifier": "B", "content": "CE"}, {"identifier": "C", "content": "$$CE{{{r_1}} \\over {({r_2} + r)}}$$ "}, {"identifier": "D", "content": "$$CE{{{r_2}} \\over {(r + {r_2})}}$$ "}] | ["D"] | null | In steady state, flow of current through capacitor will
be zero.
<br><br>Current through the circuit,
<br><br>i = $${E \over {r + {r_2}}}$$
<br><br>Potential difference through capacitor
<br><br>V<sub>c</sub> = $${Q \over C}$$ = E - ir = E - $$\left( {{E \over {r + {r_2}}}} \right)r$$
<br><br>$$ \therefore $$ Q = $$CE{... | mcq | jee-main-2017-offline | 9,377 |
yg2gJJrfgloNTeGbeAnEh | physics | capacitor | rc-circuit | In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C<sub>1</sub> as a function of time will be given by $$\left( {{C_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)$$
<br/><br/><img src="data:image/png;base64,UklGRt4HAABXRUJQVlA4INIHAABwkwCdASoAA68BP4HA3WW2MT+nIVPZI/AwCWlu/Hy... | [{"identifier": "A", "content": "$${C_1}E\\left[ {1 - \\exp \\left( { - tR/{C_1}} \\right)} \\right]$$ "}, {"identifier": "B", "content": "$${C_2}E\\left[ {1 - \\exp \\left( { - t/R{C_2}} \\right)} \\right]$$ "}, {"identifier": "C", "content": "$${C_{eq}}E\\left[ {1 - \\exp \\left( { - t/R{C_{eq}}} \\right)} \\right]$$... | ["C"] | null | Charge on capacitor at time t,
<br><br>q = q<sub>0</sub> [ 1 $$-$$ e<sup>$$-$$t/RC<sub>eq</sub></sup>]
<br><br>= C<sub>eq</sub> E [ 1 $$-$$ e<sup>$$-$$t/RC<sub>eq</sub></sup>]
<br><br>[ as $$\,\,\,\,\,\,$$ q<sub>0</sub> = C<sub>eq</sub> E]
<br><br>this charge q will be on both capacitor C<sub>1</sub> and C<sub>2</sub>... | mcq | jee-main-2018-online-16th-april-morning-slot | 9,378 |
KK0gyQH82W8shqIoykYob | physics | capacitor | rc-circuit | Determine the charge on the capacitor in the
following circuit :
<picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264101/exam_images/yeqiaq8ryxyosipsryed.webp"/><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264... | [{"identifier": "A", "content": "200\u03bcC"}, {"identifier": "B", "content": "2\u03bcC"}, {"identifier": "C", "content": "10\u03bcC"}, {"identifier": "D", "content": "60\u03bcC"}] | ["A"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264533/exam_images/or8po8laudz5neylmldl.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263634/exam_images/abznelsptw0lgst38tf8.webp"><source media="(max-wid... | mcq | jee-main-2019-online-9th-april-morning-slot | 9,379 |
EReEWAwXNFUGzLHWQn1kmkrpisf | physics | capacitor | rc-circuit | The circuit shown in the figure consists of a charged capacitor of capacity 3 $$\mu$$F and a charge of $$\mu$$C. At time t = 0, when the key is closed, the value of current flowing through the 5 M$$\Omega$$ resistor is 'x' $$\mu$$-A. The value of 'x to the nearest integer is ___________.<br/><br/><img src="data:image/p... | [] | null | 2 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265030/exam_images/vgrzbh97irbosjpbmfe3.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 18th March Morning Shift Physics - Capacitor Question 73 English Explanation">
<br><br>At time t
<... | integer | jee-main-2021-online-18th-march-morning-shift | 9,381 |
1kryupm2e | physics | capacitor | rc-circuit | <img src="data:image/png;base64,UklGRmIIAABXRUJQVlA4IFYIAABQPwCdASqtAZ4APm00mEikIqKhI1Qp4IANiWlu47APW+5SwOgnAuZ8IfzL8cfCn+3/jh1j3fv2c8yXo3b2f61/L/61/sPVz/C/xPsPtQj1f/ff43+JfpQ7PGt/oBdp/7z/HP67+pnnAfvn8i9WPpT7AH6W/33+Qfut8N/0v9AP5v5g3hH6AfAZ+Rf99/HP6L+zPv3/4/8T/n/7M+4n5f/7n8s/tXuc/7X+Mf1b9kfm09j43LFKBo8nHzprGRG6M60Bq4bG... | [{"identifier": "A", "content": "1.44 $$\\times$$ 10<sup>$$-$$4</sup> s"}, {"identifier": "B", "content": "3.33 $$\\times$$ 10<sup>$$-$$4</sup> s"}, {"identifier": "C", "content": "0.69 $$\\times$$ 10<sup>$$-$$4</sup> s"}, {"identifier": "D", "content": "0.30 $$\\times$$ 10<sup>$$-$$4</sup> s"}] | ["C"] | null | $$V = {V_0}\left( {1 - {e^{ - {t \over {RC}}}}} \right)$$<br><br>$$50 = 100\left( {1 - {e^{ - {t \over {RC}}}}} \right)$$<br><br>$$ = t = 0.69 \times {10^{ - 4}}$$ sec. | mcq | jee-main-2021-online-27th-july-morning-shift | 9,382 |
1ktafge1u | physics | capacitor | rc-circuit | The material filled between the plates of a parallel plate capacitor has resistivity 200 $$\Omega$$m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value o... | [{"identifier": "A", "content": "9.0 $$\\mu$$A"}, {"identifier": "B", "content": "9.0 mA"}, {"identifier": "C", "content": "0.9 mA"}, {"identifier": "D", "content": "0.9 $$\\mu$$A"}] | ["C"] | null | $$\rho$$ = 200 $$\Omega$$m<br><br>C = 2 $$\times$$ 10<sup>$$-$$12</sup> F<br><br>V = 40 V<br><br>K = 56<br><br>$$i = {q \over {\rho k{\varepsilon _0}}} = {{{q_0}} \over {\rho k{\varepsilon _0}}}{e^{ - {t \over {\rho k{\varepsilon _0}}}}}$$<br><br>$${i_{\max }} = {{2 \times {{10}^{ - 12}} \times 40} \over {200 \times 50... | mcq | jee-main-2021-online-26th-august-morning-shift | 9,383 |
1l54uvv2l | physics | capacitor | rc-circuit | <p>A capacitor is discharging through a resistor R. Consider in time t<sub>1</sub>, the energy stored in the capacitor reduces to half of its initial value and in time t<sub>2</sub>, the charge stored reduces to one eighth of its initial value. The ratio t<sub>1</sub>/t<sub>2</sub> will be</p> | [{"identifier": "A", "content": "1/2"}, {"identifier": "B", "content": "1/3"}, {"identifier": "C", "content": "1/4"}, {"identifier": "D", "content": "1/6"}] | ["D"] | null | <p>For a discharging capacitor when energy reduces to half the charge would become $${1 \over {\sqrt 2 }}$$ times the initial value.</p>
<p>$$ \Rightarrow {\left( {{1 \over 2}} \right)^{1/2}} = {e^{ - {t_1}/\tau }}$$</p>
<p>Similarly, $${\left( {{1 \over 2}} \right)^3} = {e^{ - {t_2}/\tau }}$$</p>
<p>$$ \Rightarrow {{{... | mcq | jee-main-2022-online-29th-june-evening-shift | 9,386 |
1lgozzkb4 | physics | capacitor | rc-circuit | <p>In the network shown below, the charge accumulated in the capacitor in steady state will be:</p>
<p><img src="data:image/png;base64,UklGRjQLAABXRUJQVlA4ICgLAACQxQCdASoAA1UCP4HA3WU2Ma4nIVJpOsAwCWlu+EMIXg15Nlvx6dtQbQ/uhxUsFZX/z0zKf/99aRKtLRbe+scJtu9/AmQt6LnSoDJGjMwvxdotfnfKKXuHzgUUvcPnAoUZNrBk2sGSlqhH/H4R9KDcJLSBCtL7K... | [{"identifier": "A", "content": "10.3 $$\\mu$$C"}, {"identifier": "B", "content": "7.2 $$\\mu$$C"}, {"identifier": "C", "content": "4.8 $$\\mu$$C"}, {"identifier": "D", "content": "12 $$\\mu$$C"}] | ["B"] | null | In steady state, capacitor behaves as open circuit.<br/><br/>
$$
\begin{aligned}
\Rightarrow \Delta V_C & =i \times 6 \Omega \\\\
& =\frac{3}{10} \times 6 \mathrm{~V} \\\\
& =1.8 \mathrm{~V} \\\\
\Rightarrow Q= & C V=7.2 \mu \mathrm{C}
\end{aligned}
$$ | mcq | jee-main-2023-online-13th-april-evening-shift | 9,388 |
1lh02cuxe | physics | capacitor | rc-circuit | <p>In this figure the resistance of the coil of galvanometer G is $$2 ~\Omega$$. The emf of the cell is $$4 \mathrm{~V}$$. The ratio of potential difference across $$\mathrm{C}_{1}$$ and $$\mathrm{C}_{2}$$ is:</p>
<p><img src="data:image/png;base64,UklGRhISAABXRUJQVlA4IAYSAADQJAGdASrzAgADP4HA2GW2MKynIZR5YsAwCWlu/AT43c9... | [{"identifier": "A", "content": "$$\\frac{5}{4}$$"}, {"identifier": "B", "content": "$$\\frac{3}{4}$$"}, {"identifier": "C", "content": "1"}, {"identifier": "D", "content": "$$\\frac{4}{5}$$"}] | ["D"] | null | At a steady state, no current would be flowing in capacitor circuit.<br/><br/>
Required $=6+2+8=16 \Omega$<br/><br/>
From Ohm's law<br/><br/>
$$
i=\frac{\mathrm{V}}{\mathrm{R}}=\frac{4}{16}=\frac{1}{4} \mathrm{~A}
$$<br/><br/>
Voltage across AC<br/><br/>
$$
\mathrm{V}_{\mathrm{AC}}=i(6+2)=\frac{1}{4} \times 8=2 \mathrm... | mcq | jee-main-2023-online-8th-april-morning-shift | 9,389 |
Ze1uZpWlVA7Tw6eN | physics | center-of-mass | cavity-problems | A circular disc of radius $$R$$ is removed from a bigger circular disc of radius $$2R$$ such that the circumferences of the discs coincide. The center of mass of the new disc is $$\alpha R$$ form the center of the bigger disc. The value of $$\alpha $$ is | [{"identifier": "A", "content": "$$1/4$$ "}, {"identifier": "B", "content": "$$1/3$$ "}, {"identifier": "C", "content": "$$1/2$$ "}, {"identifier": "D", "content": "$$1/6$$ "}] | ["B"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/jc161ivQcbdq0bi67/mIw0nNGl9d4hY8XmNmdEH1ag2TFCU/3cSxm5dD2HtlXDAQt3pMeb/image.svg" loading="lazy" alt="AIEEE 2007 Physics - Center of Mass and Collision Question 108 English Explanation">
<br>Let the mass per unit area be $$\sigma .$$ <p></p>
<br>Then the... | mcq | aieee-2007 | 9,391 |
IQCSaFT4VQpb0jBksd7k9k2k5hgj558 | physics | center-of-mass | cavity-problems | As shown in figure, when a spherical cavity
(centered at O) of radius 1 is cut out of a uniform
sphere of radius R (centered at C), the centre of
mass of remaining (shaded) part of sphere is at
G, i.e, on the surface of the cavity. R can be
detemined by the equation :
<img src="data:image/png;base64,UklGRt4LAABXRUJQVlA... | [{"identifier": "A", "content": "(R<sup>2</sup> + R \u2013 1) (2 \u2013 R) = 1"}, {"identifier": "B", "content": "(R<sup>2</sup> \u2013 R \u2013 1) (2 \u2013 R) = 1"}, {"identifier": "C", "content": "(R<sup>2</sup> \u2013 R + 1) (2 \u2013 R) = 1"}, {"identifier": "D", "content": "(R<sup>2</sup> + R + 1) (2 \u2013 R) = ... | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267225/exam_images/cyltnmcnp7muxsqpivj7.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Evening Slot Physics - Center of Mass and Collision Question 73 English Explanation">
... | mcq | jee-main-2020-online-8th-january-evening-slot | 9,392 |
W3ptL0MlNlW9oo6Pfdjgy2xukexyqtgn | physics | center-of-mass | cavity-problems | A square shaped hole of side l = $${a \over 2}$$ is carved
out at a distance d = $${a \over 2}$$ from the centre ‘O’ of
a uniform circular disk of radius a. If the
distance of the centre of mass of the
remaining portion form O is
$$ - {a \over X}$$ , value of X (to
the nearest integer) is :
<img src="data:image/png;bas... | [] | null | 23 | X<sub>com</sub> = $${{\sigma \pi {a^2} \times 0 - \sigma .{{{a^2}} \over 4}.d} \over {\sigma \pi {a^2} - \sigma .{{{a^2}} \over 4}}}$$
<br><br>= $${{ - {{{a^2}} \over 4}.d} \over {\pi {a^2} - {{{a^2}} \over 4}}}$$
<br><br>= $${{ - d} \over {4\pi - 1}}$$ = $${{ - a} \over {2\left( {4\pi - 1} \right)}}$$
<br><br>$$ \th... | integer | jee-main-2020-online-2nd-september-evening-slot | 9,393 |
leZIcOyf1UrBecKAOk1klrok99c | physics | center-of-mass | cavity-problems | A circular hole of radius $$\left( {{a \over 2}} \right)$$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :<br/><br/><img src="data:image/png;base64,UklGRsYSAABXRUJQVlA4ILoSAABwGAGdASoAA/cCP4HA2mW2MC0nIXIZEsAwCWlu8mu7xgdJt... | [{"identifier": "A", "content": "$${1 \\over 6}a$$"}, {"identifier": "B", "content": "$${2 \\over 3}a$$"}, {"identifier": "C", "content": "$${5 \\over 6}a$$"}, {"identifier": "D", "content": "$${10 \\over 11}a$$"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263893/exam_images/rxklmif5qkodbe7eurbo.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 24th February Evening Shift Physics - Center of Mass and Collision Question 57 English Explanation... | mcq | jee-main-2021-online-24th-february-evening-slot | 9,394 |
DTbqjQLkohJDnpSy | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass $${1 \over 3}$$ $$M$$ and a body $$C$$ of mass $${2 \over 3}$$ $$M.$$ The center of mass of bodies $$B$$ and $$C$$ taken together shifts compared to that of bodies $$B$$ and $$C$$ taken together shift... | [{"identifier": "A", "content": "does not shift "}, {"identifier": "B", "content": "depends on height of breaking "}, {"identifier": "C", "content": "body $$B$$ "}, {"identifier": "D", "content": "body $$C$$ "}] | ["A"] | null | The center of mass does not shift as no external force is applied horizontally. So the center of mass of the system continues its original path. It is only the internal forces which comes into play while breaking. | mcq | aieee-2005 | 9,395 |
HTjKEbH5uWpwYOVP | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $$'\,\,\overrightarrow F \,\,'$$ is applied at the point $$P$$ parallel to $$AB,$$ such that the object has only the translational motion without rotation. Find the location of $$P$$ with respect to $$C.$$
<img src="data:image/p... | [{"identifier": "A", "content": "$${3 \\over 2}L$$"}, {"identifier": "B", "content": "$${2 \\over 3}L$$"}, {"identifier": "C", "content": "$$L$$ "}, {"identifier": "D", "content": "$${4 \\over 3}L$$"}] | ["D"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/QfWVHVIJRoKlCJXbX/EMCj9vhIhZlb4DCOlEgs9iTUsIJVd/CWRnPXK3ofrOTkpa5s8vB5/image.svg" loading="lazy" alt="AIEEE 2005 Physics - Center of Mass and Collision Question 104 English Explanation">
<br>This is a case of translation motion without rotation, the forc... | mcq | aieee-2005 | 9,396 |
Psq3eNeeleoaRu4P | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mass/length) varies with $$x$$ as $$k{\left( {{x \over L}} \right)^n},$$ where $$n$$ can be zero or any positive number. If the position $${X_{CM}}$$ of the center of mass of the rod is plotted against $... | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266894/exam_images/moawxdrgcvkt3f6tv6yw.webp\" loading=\"lazy\" alt=\"AIEEE 2008 Physics - Center of Mass and Collision Question 103 English Option 1\"> "}, {"identifier": "B", "content": "<img cl... | ["A"] | null | <p>Given The linear mass density $$\lambda = k{\left( {{x \over L}} \right)^n}$$</p>
<br><br>$${x_{CM}} = {{\int\limits_0^L {x{\mkern 1mu} dm} } \over {\int\limits_0^L {dm} }}$$
<br><br>$$ = {{\int\limits_0^L {x\left( {\lambda {\mkern 1mu} dx} \right)} } \over {\int\limits_0^L {\lambda {\mkern 1mu} dx} }}$$
<br><br>$... | mcq | aieee-2008 | 9,397 |
omQyOEUcRZBHaz0FivKQg | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $${{BC} \over {AB}}$$ is close to :
<br/><br/><img src="data:image/png;base64,UklGRnAGAABXRUJQVlA4IGQGAACQbQCdASoAA0EBP4HA22Y2MK2nITHIusAwCWlu8p8dxWvIj187zt/AjM9iNtE31+i3FMdNWniA75eVcvbE1aeIDvm8QHfN4gO+X7B/lRWw8gvQ... | [{"identifier": "A", "content": "1.85"}, {"identifier": "B", "content": "1.37"}, {"identifier": "C", "content": "1.5"}, {"identifier": "D", "content": "3"}] | ["B"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l82x6o37/eda26380-1a00-4434-87cf-4900d2f5fc69/b1034c30-34e2-11ed-b84c-a3c7c2456516/file-1l82x6o38.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l82x6o37/eda26380-1a00-4434-87cf-4900d2f5fc69/b1034c30-34e2-11ed-b84c-a3c7c2456516/fi... | mcq | jee-main-2016-online-10th-april-morning-slot | 9,399 |
13Mw2X2WaU5MnrKO4acsn | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | A uniform rectangular thin sheet ABCD of
mass M has length a and breadth b, as shown
in the figure. If the shaded portion HBGO is
cut-off, the coordinates of the centre of mass
of the remaining portion will be :-
<img src="data:image/png;base64,UklGRuYXAABXRUJQVlA4INoXAADQ0wCdASrsAocBP4G+12S2MCwnI7NJWsAwCWlu/HyZxL0HZ19... | [{"identifier": "A", "content": "$$\\left( {{{5a} \\over 3},{{5b} \\over 3}} \\right)$$"}, {"identifier": "B", "content": "$$\\left( {{{2a} \\over 3},{{2b} \\over 3}} \\right)$$"}, {"identifier": "C", "content": "$$\\left( {{{5a} \\over 12},{{5b} \\over 12}} \\right)$$"}, {"identifier": "D", "content": "$$\\left( {{{3a... | ["C"] | null | X- coordinate of CM of remaining sheet<br>
$${X_{cm}} = {{MX - mx} \over {M - m}}$$<br><br>
= $${{\left( {4m} \right) \times \left( {{a \over 2}} \right) - M\left( {{{3a} \over 4}} \right)} \over {4m - m}} = {{5a} \over {12}}$$<br><br>
Similarly y<sub>cm</sub> = $${{5b} \over {12}}$$<br><br>
$$ \therefore $$ $$CM\left(... | mcq | jee-main-2019-online-8th-april-evening-slot | 9,400 |
oyneWIET0DZ1OgQbK57k9k2k5gw6mci | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | The coordinates of centre of mass of a uniform
flag shaped lamina (thin flat plate) of mass 4kg.
(The coordinates of the same are shown in
figure) are :
<img src="data:image/png;base64,UklGRjYJAABXRUJQVlA4ICoJAACQQgCdASo3AewAPm02mEikIqKhIrKZwIANiWlu9kAYdrkAZ2ddf6Lfyf8gPBf+3dGp6O9qvTX+Gtap+C/k39s/4n9F+kf7N+gHi/wAvWv+i/j... | [{"identifier": "A", "content": "(0.75m, 1.75m)"}, {"identifier": "B", "content": "(1m, 1.75m)"}, {"identifier": "C", "content": "(0.75m, 0.75m)"}, {"identifier": "D", "content": "(1.25m, 1.50m)"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267588/exam_images/ma7kpbl45yuc0i0lpykp.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Morning Slot Physics - Center of Mass and Collision Question 75 English Explanation">
... | mcq | jee-main-2020-online-8th-january-morning-slot | 9,401 |
u9CwJJkzFTx8gwZ5IU7k9k2k5kv9tjp | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | A rod of length L has non-uniform linear mass
<br/>density given by $$\rho $$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$
, where a
<br/>and b are constants and 0 $$ \le $$ x $$ \le $$ L. The value
<br/>of x for the centre of mass of the rod is at : | [{"identifier": "A", "content": "$${3 \\over 2}\\left( {{{a + b} \\over {2a + b}}} \\right)L$$"}, {"identifier": "B", "content": "$${4 \\over 3}\\left( {{{a + b} \\over {2a + 3b}}} \\right)L$$"}, {"identifier": "C", "content": "$${3 \\over 4}\\left( {{{2a + b} \\over {3a + b}}} \\right)L$$"}, {"identifier": "D", "conte... | ["C"] | null | $$\rho $$ = a + b$${\left( {{x \over L}} \right)^2}$$
<br><br>dm = $$\rho $$dx = $$\left( {a + b{{{x^2}} \over {{L^2}}}} \right)dx$$
<br><br>M = $$\int {dm} $$ = $$\int\limits_0^L {\left( {a + b{{{x^2}} \over {{L^2}}}} \right)dx} $$
<br><br>X<sub>com</sub> = $${{\int {xdm} } \over {\int {dm} }}$$
<br><br>= $${{\int\lim... | mcq | jee-main-2020-online-9th-january-evening-slot | 9,402 |
9Dk8wkdWL3DydwK85Ajgy2xukg0j85o7 | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then
value of x is __________.
| [] | null | 3 | As we know c.o.m. or hemisphere = $${{3R} \over 8}$$
<br><br>$$ \therefore $$ x = $${{3R} \over 8}$$ = $${{3 \times 8} \over 8}$$ = 3 cm | integer | jee-main-2020-online-6th-september-evening-slot | 9,403 |
NEz5V3xfQIgv74eD421kmkc1n3y | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $${x \over 3}{a \over \pi },{x \over 3}{a \over \pi }$$ where x is _____________. (Round off to the Nearest Integer).<br/><br/>[a is an area as shown in the... | [] | null | 4 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263841/exam_images/zfrppxadtlodhn3jncli.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Evening Shift Physics - Center of Mass and Collision Question 50 English Explanation">
... | integer | jee-main-2021-online-17th-march-evening-shift | 9,404 |
1krsxosyr | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $$\left( {0,{{xR} \over \pi }} \right)$$. Then, the value of | x | is ______________. | [] | null | 2 | Centre of mass of half ring is located at a distance $${{2R} \over \pi }$$ from centre of the ring on its axis of symmetry so position of centre of mass in the given question will be $$\left( {0,{{xR} \over \pi }} \right)$$<br><br>$$\Rightarrow$$ | x | = 2 | integer | jee-main-2021-online-22th-july-evening-shift | 9,405 |
1l6ntkra9 | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | <p>The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $$\rho=\rho_{0}\left(1-\frac{x^{2}}{L^{2}}\right) \mathrm{kg} / \mathrm{m}$$ and length L (in meter) is $$\frac{3 L}{\alpha} \mathrm{m}$$. The value of $$\alpha$$ is ___________. (where x is the distance from end A)</p> | [] | null | 8 | <p>$$\rho = {\rho _0}\left( {1 - {{{x^2}} \over {{L^2}}}} \right)$$ kg/m</p>
<p>$${x_{cm}} = {{A\int\limits_0^L {{\rho _0}\left( {1 - {{{x^2}} \over {{L^2}}}} \right)x\,dx} } \over {A\int\limits_0^L {{\rho _0}\left( {1 - {{{x^2}} \over {{L^2}}}} \right)\,dx} }}$$</p>
<p>$${x_{cm}} = {{{{{L^2}} \over 2} - {{{L^2}} \ove... | integer | jee-main-2022-online-28th-july-evening-shift | 9,406 |
lv5gt54p | physics | center-of-mass | center-of-mass-of-continuous-mass-distribution | <p>A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.</p>
<p><img src="data:image/png;base64,UklGRj4bAABXRUJQVlA4IDIbAABQRQGdASoAA/0BP4G412A2LzilolGcExAwCWlu4XHhG/OZ... | [] | null | 15 | <p>$$\begin{array}{ll}
x_{\mathrm{cm}}=1.5 & \\
M_{+}=6 \sigma & y_{+}=1 \\
M_{-}=-\sigma & y_{-}=1.5
\end{array}$$</p>
<p>$$\begin{aligned}
& y_{\mathrm{cm}}=\frac{6 \sigma \times 1+(-\sigma) \times 1.5}{6 \sigma-\sigma} \\
& =\frac{6-1.5}{5}=\frac{4.5}{5}=0.9 \\
& \frac{x}{y}=\frac{1.5}{0.9}=\frac{15}{9}
\end{aligned... | integer | jee-main-2024-online-8th-april-morning-shift | 9,407 |
VLHK6KOaUxPayjKB | physics | center-of-mass | center-of-mass-of-discrete-particles | Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass through a distance $$d,$$ by what distance should the second particle is moved, so as to keep the center of mass at the same position? | [{"identifier": "A", "content": "$${{{m_2}} \\over {{m_1}}}\\,\\,d$$ "}, {"identifier": "B", "content": "$${{{m_1}} \\over {{m_1} + {m_2}}}d$$ "}, {"identifier": "C", "content": "$${{{m_1}} \\over {{m_2}}}d$$ "}, {"identifier": "D", "content": "$$d$$ "}] | ["C"] | null | Initially,
<br><img class="question-image" src="https://imagex.cdn.examgoal.net/MmP0ascyNLHCptltH/PafY176kaTqUDIfLmTGROM52Rc6tA/jYuZQjt2765EWW34bkSVE4/image.svg" loading="lazy" alt="AIEEE 2006 Physics - Center of Mass and Collision Question 109 English Explanation 1">
<br>$$0 = {{{m_1}\left( { - {x_1}} \right) + {m_2}... | mcq | aieee-2006 | 9,408 |
5DJWlHhixjPCIACFbkQHv | physics | center-of-mass | center-of-mass-of-discrete-particles | The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :
<br/><br/><img src="data:image/png;base64,UklGRpYFAABXRUJQVlA4IIoFAAAwZQCdASqsAqcBP4HA4GY2ML+nIjKIU/AwCWlu4XShG/P58xPr3ZyjxZJSu2eW76P3uEv5u6aCfzC3YvM9ARl10... | [{"identifier": "A", "content": "$${\\overrightarrow r _{cm}}\\, = {{11} \\over 8}L\\,\\,\\widehat x + {8 \\over 8}L\\widehat y$$"}, {"identifier": "B", "content": "$${\\overrightarrow r _{cm}}\\, = {5 \\over 8}L\\,\\,\\widehat x + {{13} \\over 8}L\\widehat y$$"}, {"identifier": "C", "content": "$${\\overrightarrow r _... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263322/exam_images/luzznjmlywhz6tggqsgg.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th January Morning Slot Physics - Center of Mass and Collision Question 90 English Explanation... | mcq | jee-main-2019-online-12th-january-morning-slot | 9,410 |
STSXzsJAOJzP7YaPPt3rsa0w2w9jx7p3q1v | physics | center-of-mass | center-of-mass-of-discrete-particles | Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side
1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :
<img src="data:image/png;base64,UklGRnoMAABXRUJQVlA4IG4MAAAwcgCdASrsAiQBP4HA3GW2MS2nIfNI0sAwCWlu/HyZVOtQ3f1R/x/br/xciCb87G+AE... | [{"identifier": "A", "content": "$$\\left( {{{\\sqrt 3 } \\over 4}m,{5 \\over {12}}m} \\right)$$"}, {"identifier": "B", "content": "$$\\left( {{7 \\over {12}}m,{{\\sqrt 3 } \\over 8}m} \\right)$$"}, {"identifier": "C", "content": "$$\\left( {{7 \\over {12}}m,{{\\sqrt 3 } \\over 4}m} \\right)$$"}, {"identifier": "D", "c... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265711/exam_images/jrv6l5aznvgblmaubaem.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th April Evening Slot Physics - Center of Mass and Collision Question 77 English Explanation">... | mcq | jee-main-2019-online-12th-april-evening-slot | 9,411 |
zTlAV3WQ2y9aq5LyEf7k9k2k5dp58vh | physics | center-of-mass | center-of-mass-of-discrete-particles | Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:
<img src="data:image/png;base64,UklGRloKAABXRUJQVlA4IE4KAABQRQCdASosAcYAPm0ylkkkIqIhInHKWIANiWlu4XHF7... | [{"identifier": "A", "content": "2.0 cm right and 0.9 cm above 1 kg mass"}, {"identifier": "B", "content": "0.9 cm right and 2.0 cm above 1 kg mass"}, {"identifier": "C", "content": "0.6 cm right and 2.0 cm above 1 kg mass"}, {"identifier": "D", "content": "1.5 cm right and 1.2 cm above 1 kg mass"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266733/exam_images/kbz2lpgpbroh0jahnqtm.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 7th January Morning Slot Physics - Center of Mass and Collision Question 76 English Explanation">
... | mcq | jee-main-2020-online-7th-january-morning-slot | 9,412 |
1l57pqga0 | physics | center-of-mass | center-of-mass-of-discrete-particles | <p>Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre ... | [{"identifier": "A", "content": "4 cm towards the 10 kg block"}, {"identifier": "B", "content": "2 cm away from the 10 kg block"}, {"identifier": "C", "content": "2 cm towards the 10 kg block"}, {"identifier": "D", "content": "4 cm away from the 10 kg block"}] | ["C"] | null | <p>For COM to remain unchanged,</p>
<p>m<sub>1</sub>x<sub>1</sub> = m<sub>2</sub>x<sub>2</sub></p>
<p>$$\Rightarrow$$ 10 $$\times$$ 6 = 30 $$\times$$ x<sub>2</sub></p>
<p>$$\Rightarrow$$ x<sub>2</sub> = 2 cm towards 10 kg block.</p> | mcq | jee-main-2022-online-27th-june-morning-shift | 9,414 |
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