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select a speed of? ( b ) what is the voltage between the plates if they are separated by 1. 00 cm? 18. an electron in a tv crt moves with a speed of, in a direction perpendicular to the earth ’ s field, which has a strength of. ( a ) what strength electric field must be applied perpendicular to the earth ’ s field to m... | openstax_college_physics_2e-web_7zesafu | [
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0. 250 - t field. what is the separation between their paths when they hit a target after traversing a semicircle? ( b ) discuss whether this distance between their paths seems to be big enough to be practical in the separation of uranium - 235 from uranium - 238. 994 22 • problems & exercises access for free at openst... | openstax_college_physics_2e-web_7zesafu | [
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22. 6 the hall effect 22. a large water main is 2. 50 m in diameter and the average water velocity is 6. 00 m / s. find the hall voltage produced if the pipe runs perpendicular to the earth ’ s field. 23. what hall voltage is produced by a 0. 200 - t field applied across a 2. 60 - cm - diameter aorta when blood velocit... | openstax_college_physics_2e-web_7zesafu | [
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, and subjected to the same magnetic field is inversely proportional to their diameters. ( hint : consider how drift velocity depends on wire diameter. ) 30. a patient with a pacemaker is mistakenly being scanned for an mri image. a 10. 0 - cm - long section of pacemaker wire moves at a speed of 10. 0 cm / s perpendicu... | openstax_college_physics_2e-web_7zesafu | [
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22. 7 magnetic force on a current - carrying conductor 31. what is the direction of the magnetic force on the current in each of the six cases in figure 22. 50? figure 22. 50 32. what is the direction of a current that experiences the magnetic force shown in each of the three cases in figure 22. 51, assuming the curren... | openstax_college_physics_2e-web_7zesafu | [
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4. 00 cm of wire in the field. what is the average field strength? 38. ( a ) a 0. 750 - m - long section of cable carrying current to a car starter motor makes an angle of with the earth ’ s field. what is the current when the wire experiences a force of? ( b ) if you run the wire between the poles of a strong horsesho... | openstax_college_physics_2e-web_7zesafu | [
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2. 40 n? ( b ) what is the force on the wire if it is rotated to make an angle of with the field? 40. the force on the rectangular loop of wire in the magnetic field in figure 22. 53 can be used to measure field strength. the field is uniform, and the plane of the loop is perpendicular to the field. ( a ) what is the d... | openstax_college_physics_2e-web_7zesafu | [
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22. 8 torque on a current loop : motors and meters 41. ( a ) by how many percent is the torque of a motor decreased if its permanent magnets lose 5. 0 % of their strength? ( b ) how many percent would the current need to be increased to return the torque to original values? 42. ( a ) what is the maximum torque on a 150... | openstax_college_physics_2e-web_7zesafu | [
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when viewed from the east. the earth ’ s field here is due north, parallel to the ground, with a strength of. what are the direction and magnitude of the torque on the loop? ( b ) does this device have any practical applications as a motor? 49. repeat exercise 22. 41, but with the loop lying flat on the ground with its... | openstax_college_physics_2e-web_7zesafu | [
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5. 00 a to a headlight. ( a ) how far apart are the wires? ( b ) are the currents in the same direction? 54. an ac appliance cord has its hot and neutral wires separated by 3. 00 mm and carries a 5. 00 - a current. ( a ) what is the average force per meter between the wires in the cord? ( b ) what is the maximum force ... | openstax_college_physics_2e-web_7zesafu | [
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22. 11 more applications of magnetism 58. indicate whether the magnetic field created in each of the three situations shown in figure 22. 56 is into or out of the page on the left and right of the current. figure 22. 56 59. what are the directions of the fields in the center of the loop and coils shown in figure 22. 57... | openstax_college_physics_2e-web_7zesafu | [
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carrying 150 a, must you be to experience a field less than the earth ’ s assume a long straight wire carries the current. ( in practice, the body of your car shields the dashboard compass. ) 67. measurements affect the system being measured, such as the current loop in figure 22. 53. ( a ) estimate the field the loop ... | openstax_college_physics_2e-web_7zesafu | [
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. calculate the size of the magnetic field 20 m below a high voltage power line. the line carries 450 mw at a voltage of 300, 000 v. 73. integrated concepts ( a ) a pendulum is set up so that its bob ( a thin copper disk ) swings between the poles of a permanent magnet as shown in figure 22. 60. what is the magnitude a... | openstax_college_physics_2e-web_7zesafu | [
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in exercise 22. 59, and assuming the force is uniformly applied to the fluid, calculate the pressure created in ( b ) is this a significant fraction of an atmosphere? 78. integrated concepts ( a ) calculate the maximum torque on a 50 - turn, | openstax_college_physics_2e-web_7zesafu | [
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1. 50 cm radius circular current loop carrying in a 0. 500 - t field. ( b ) if this coil is to be used in a galvanometer that reads full scale, what force constant spring must be used, if it is attached 1. 00 cm from the axis of rotation and is stretched by the arc moved? 79. integrated concepts a current balance used ... | openstax_college_physics_2e-web_7zesafu | [
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it deflected from its path by the magnetic force, after traveling 30. 0 m horizontally? ( b ) would you suggest this as a secret technique for a pitcher to throw curve balls? 83. integrated concepts ( a ) what is the direction of the force on a wire carrying a current due east in a location where the earth ’ s field is... | openstax_college_physics_2e-web_7zesafu | [
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120 - v power by moving a 1. 00 - m - long wire perpendicular to the earth ’ s field. ( a ) find the speed with which the wire must move. ( b ) what is unreasonable about this result? ( c ) which assumption is responsible? 88. unreasonable results frustrated by the small hall voltage obtained in blood flow measurements... | openstax_college_physics_2e-web_7zesafu | [
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earth, for example ). construct a problem in which you calculate the maximum torque on a current - carrying loop in a magnetic field. among the things to be considered are the size of the coil, the number of loops it has, the current you pass through the coil, and the size of the field you wish to detect. discuss wheth... | openstax_college_physics_2e-web_7zesafu | [
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23. 12 rlc series ac circuits nature ’ s displays of symmetry are beautiful and alluring. a butterfly ’ s wings exhibit an appealing symmetry in a complex system. ( see figure 23. 2. ) the laws of physics display symmetries at the most basic level — these symmetries are a source of wonder and imply deeper meaning. sinc... | openstax_college_physics_2e-web_7zesafu | [
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from charging by induction, which utilizes the coulomb force. today, currents induced by magnetic fields are essential to our technological society. the ubiquitous generator — found in automobiles, on bicycles, in nuclear power plants, and so on — uses magnetism to generate current. other devices that use magnetism to ... | openstax_college_physics_2e-web_7zesafu | [
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23. 1 induced emf and magnetic flux learning objectives by the end of this section, you will be able to : • calculate the flux of a uniform magnetic field through a loop of arbitrary orientation. • describe methods to produce an electromotive force ( emf ) with a magnetic field or magnet and a loop of wire. the apparat... | openstax_college_physics_2e-web_7zesafu | [
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remains closed or open. an experiment easily performed and often done in physics labs is illustrated in figure 23. 4. an emf is induced in the coil when a bar magnet is pushed in and out of it. emfs of opposite signs are produced by motion in opposite directions, and the emfs are also reversed by reversing poles. the s... | openstax_college_physics_2e-web_7zesafu | [
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23. 1 • induced emf and magnetic flux 1005 figure 23. 5 rotation of a coil in a magnetic field produces an emf. this is the basic construction of a generator, where work done to turn the coil is converted to electric energy. note the generator is very similar in construction to a motor. so we see that changing the magn... | openstax_college_physics_2e-web_7zesafu | [
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23. 2 faraday ’ s law of induction : lenz ’ s law learning objectives by the end of this section, you will be able to : • calculate emf, current, and magnetic fields using faraday ’ s law. • explain the physical results of lenz ’ s law faraday ’ s and lenz ’ s law faraday ’ s experiments showed that the emf induced by ... | openstax_college_physics_2e-web_7zesafu | [
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of lenz ’ s law — induction opposes any change in flux. ( b ) and ( c ) are two other situations. verify for yourself that the direction of the induced shown indeed opposes the change in flux and that the current direction shown is consistent with rhr - 2. 23. 2 problem - solving strategy for lenz ’ s law to use lenz ’... | openstax_college_physics_2e-web_7zesafu | [
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23. 2 • faraday ’ s law of induction : lenz ’ s law 1007 for practice, apply these steps to the situations shown in figure 23. 7 and to others that are part of the following text material. applications of electromagnetic induction there are many applications of faraday ’ s law of induction, as we will explore in this c... | openstax_college_physics_2e-web_7zesafu | [
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hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance. ( the discovery that weak changes in a magnetic field in a thin film of iron and chromium could bring about much larger changes in electrical resistance was one of the first large successes of nan... | openstax_college_physics_2e-web_7zesafu | [
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simulation. a host of disorders, including depression and hallucinations can be traced to irregular localized electrical activity in the brain. in transcranial magnetic stimulation, a rapidly varying and very localized magnetic field is placed close to certain sites identified in the brain. weak electric currents are i... | openstax_college_physics_2e-web_7zesafu | [
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as stated by, but without the minus sign that indicates direction : solution we are given that and, but we must determine the change in flux before we can find emf. making connections : conservation of energy lenz ’ s law is a manifestation of the conservation of energy. the induced emf produces a current that opposes ... | openstax_college_physics_2e-web_7zesafu | [
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23. 2 • faraday ’ s law of induction : lenz ’ s law 1009 since the area of the loop is fixed, we see that now, since it was given that changes from 0. 0500 to 0. 250 t. the area of the loop is. thus, entering the determined values into the expression for emf gives discussion while this is an easily measured voltage, it... | openstax_college_physics_2e-web_7zesafu | [
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23. 3 motional emf learning objectives by the end of this section, you will be able to : • calculate emf, force, magnetic field, and work due to the motion of an object in a magnetic field. as we have seen, any change in magnetic flux induces an emf opposing that change — a process known as induction. motion is one of ... | openstax_college_physics_2e-web_7zesafu | [
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23. 6 1010 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org figure 23. 10 ( a ) a motional is induced between the rails when this rod moves to the right in the uniform magnetic field. the magnetic field is into the page, perpendicular to the moving rod and rails ... | openstax_college_physics_2e-web_7zesafu | [
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23. 3 • motional emf 1011 to find the direction of the induced field, the direction of the current, and the polarity of the induced emf, we apply lenz ’ s law as explained in faraday's law of induction : lenz's law. ( see figure 23. 10 ( b ). ) flux is increasing, since the area enclosed is increasing. thus the induced... | openstax_college_physics_2e-web_7zesafu | [
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by moving at orbital speed through the earth ’ s field. this emf could be used to convert some of the shuttle ’ s kinetic and potential energy into electrical energy if a complete circuit could be made. to complete the circuit, the stationary ionosphere was to supply a return path for the current to flow. ( the ionosph... | openstax_college_physics_2e-web_7zesafu | [
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by a return path through the stationary ionosphere. calculate the motional emf induced along a 20. 0 km long conductor moving at an orbital speed of 7. 80 km / s perpendicular to the earth ’ s magnetic field. strategy this is a straightforward application of the expression for motional emf —. solution entering the give... | openstax_college_physics_2e-web_7zesafu | [
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23. 4 • eddy currents and magnetic damping 1013 that current as an eddy current. eddy currents can produce significant drag, called magnetic damping, on the motion involved. consider the apparatus shown in figure 23. 12, which swings a pendulum bob between the poles of a strong magnet. ( this is another favorite physic... | openstax_college_physics_2e-web_7zesafu | [
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uniform, since the flux remains constant in this region. but when the plate leaves the field on the right, flux decreases, causing an eddy current in the clockwise direction that, again, experiences a force to the left, further slowing the motion. a similar analysis of what happens when the plate swings from the right ... | openstax_college_physics_2e-web_7zesafu | [
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. with magnetic damping, drag is proportional to speed and becomes zero at zero velocity. thus the oscillations are quickly damped, after which the damping force disappears, allowing the balance to be very sensitive. ( see figure 23. 15. ) in most balances, magnetic damping is accomplished with a conducting disc that r... | openstax_college_physics_2e-web_7zesafu | [
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23. 4 • eddy currents and magnetic damping 1015 figure 23. 16 metals can be separated from other trash by magnetic drag. eddy currents and magnetic drag are created in the metals sent down this ramp by the powerful magnet beneath it. nonmetals move on. other major applications of eddy currents are in metal detectors an... | openstax_college_physics_2e-web_7zesafu | [
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field is varied rapidly producing eddy currents in the base of the pot, causing the pot and its contents to increase in temperature. induction cooktops have high efficiencies and good response times but the base of the pot needs to be ferromagnetic, iron or steel for induction to work. 23. 5 electric generators learnin... | openstax_college_physics_2e-web_7zesafu | [
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23. 5 • electric generators 1017 figure 23. 19 when this generator coil is rotated through one - fourth of a revolution, the magnetic flux changes from its maximum to zero, inducing an emf. strategy we use faraday ’ s law of induction to find the average emf induced over a time : we know that and, and so we must determ... | openstax_college_physics_2e-web_7zesafu | [
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23. 14 1018 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org figure 23. 20 a generator with a single rectangular coil rotated at constant angular velocity in a uniform magnetic field produces an emf that varies sinusoidally in time. note the generator is similar ... | openstax_college_physics_2e-web_7zesafu | [
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it now seems reasonable that ac voltage is sinusoidal. 23. 15 23. 16 23. 17 23. 18 23. 19 23. 20 | openstax_college_physics_2e-web_7zesafu | [
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23. 5 • electric generators 1019 figure 23. 21 the emf of a generator is sent to a light bulb with the system of rings and brushes shown. the graph gives the emf of the generator as a function of time. is the peak emf. the period is, where is the frequency. note that the script e stands for emf. the fact that the peak ... | openstax_college_physics_2e-web_7zesafu | [
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104. 7 rad / s is exactly 1000 rpm. we substitute this value for and the information from the previous example into, yielding discussion the maximum emf is greater than the average emf of 131 v found in the previous example, as it should be. in real life, electric generators look a lot different than the figures in thi... | openstax_college_physics_2e-web_7zesafu | [
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23. 6 • back emf 1021 whether the shaft is turned by an external input, like a belt drive, or by the action of the motor itself. that is, when a motor is doing work and its shaft is turning, an emf is generated. lenz ’ s law tells us the emf opposes any change, so that the input emf that powers the motor will be oppose... | openstax_college_physics_2e-web_7zesafu | [
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the larger current can overheat it ( via resistive power in the coil, ), perhaps even burning it out. on the other hand, if there is no mechanical load on the motor, it will increase its angular velocity until the back emf is nearly equal to the driving emf. then the motor uses only enough energy to overcome friction. ... | openstax_college_physics_2e-web_7zesafu | [
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23. 7 transformers learning objectives by the end of this section, you will be able to : • explain how a transformer works. • calculate voltage, current, and / or number of turns given the other quantities. transformers do what their name implies — they transform voltages from one value to another ( the term voltage is... | openstax_college_physics_2e-web_7zesafu | [
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— see figure 23. 27 — is based on faraday ’ s law of induction and is very similar in construction to the apparatus faraday used to demonstrate magnetic fields could cause currents. the two coils are called the primary and secondary coils. in normal use, the input voltage is placed on the primary, and the secondary pro... | openstax_college_physics_2e-web_7zesafu | [
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23. 7 • transformers 1023 figure 23. 27 a typical construction of a simple transformer has two coils wound on a ferromagnetic core that is laminated to minimize eddy currents. the magnetic field created by the primary is mostly confined to and increased by the core, which transmits it to the secondary coil. any change ... | openstax_college_physics_2e-web_7zesafu | [
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, depending on the ratio of the number of loops in their coils. some transformers even provide a variable output by allowing connection to be made at different points on the secondary coil. a step - up transformer is one that increases voltage, whereas a step - down transformer decreases voltage. assuming, as we have, ... | openstax_college_physics_2e-web_7zesafu | [
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23. 27 1024 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org combining this with, we find that is the relationship between the output and input currents of a transformer. so if voltage increases, current decreases. conversely, if voltage decreases, current increa... | openstax_college_physics_2e-web_7zesafu | [
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. as the switch is opened and closed, the secondary produces a voltage like that in figure 23. 28. this is not really a practical alternative, and ac is in common use wherever it is necessary to increase or decrease voltages. 23. 28 23. 29 23. 30 23. 31 | openstax_college_physics_2e-web_7zesafu | [
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23. 7 • transformers 1025 figure 23. 28 transformers do not work for pure dc voltage input, but if it is switched on and off as on the top graph, the output will look something like that on the bottom graph. this is not the sinusoidal ac most ac appliances need. example 23. 6 calculating characteristics of a step - dow... | openstax_college_physics_2e-web_7zesafu | [
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electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org secondary coil needs to be converted into dc. this is done using something called a rectifier, which uses devices called diodes that allow only a one - way flow of current. transformers have many applications in electri... | openstax_college_physics_2e-web_7zesafu | [
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23. 8 electrical safety : systems and devices learning objectives by the end of this section, you will be able to : • explain how various modern safety features in electric circuits work, with an emphasis on how induction is employed. electricity has two hazards. a thermal hazard occurs when there is electrical overhea... | openstax_college_physics_2e-web_7zesafu | [
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23. 8 • electrical safety : systems and devices 1027 figure 23. 30 the three - wire system connects the neutral wire to the earth at the voltage source and user location, forcing it to be at zero volts and supplying an alternative return path for the current through the earth. also grounded to zero volts is the case of... | openstax_college_physics_2e-web_7zesafu | [
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. figure 23. 31 the standard three - prong plug can only be inserted in one way, to assure proper function of the three - wire system. a note on insulation color - coding : insulating plastic is color - coded to identify live / hot, neutral and ground wires but these codes vary around the world. live / hot wires may be... | openstax_college_physics_2e-web_7zesafu | [
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, such as power tools with impact resistant plastic cases, and are called doubly insulated. modern two - prong plugs can be inserted into the asymmetric standard outlet in only one way, to ensure proper connection of live / hot and neutral wires. figure 23. 32 worn insulation allows the live / hot wire to come into dir... | openstax_college_physics_2e-web_7zesafu | [
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23. 8 • electrical safety : systems and devices 1029 current, although current does not necessarily pass from the resistor to the case. figure 23. 33 ac currents can induce an emf on the case of an appliance. the voltage can be large enough to cause a shock. if the case is grounded, the induced emf is kept near zero. a... | openstax_college_physics_2e-web_7zesafu | [
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using both to induce an emf in the same coil. if the currents are equal, they will induce equal but opposite emfs. another induction - based safety device is the isolation transformer, shown in figure 23. 36. most isolation transformers have equal input and output voltages. their function is to put a large resistance b... | openstax_college_physics_2e-web_7zesafu | [
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an inductor. • calculate the emf generated in an inductor. inductors induction is the process in which an emf is induced by changing magnetic flux. many examples have been discussed so far, some more effective than others. transformers, for example, are designed to be particularly effective at | openstax_college_physics_2e-web_7zesafu | [
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23. 9 • inductance 1031 inducing a desired voltage and current with very little loss of energy to other forms. is there a useful physical quantity related to how “ effective ” a given device is? the answer is yes, and that physical quantity is called inductance. mutual inductance is the effect of faraday ’ s law of ind... | openstax_college_physics_2e-web_7zesafu | [
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. a large mutual inductance may or may not be desirable. we want a transformer to have a large mutual inductance. but an appliance, such as an electric clothes dryer, can induce a dangerous emf on its case if the mutual inductance between its coils and the case is large. one way to reduce mutual inductance is to counte... | openstax_college_physics_2e-web_7zesafu | [
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23. 35 1032 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org figure 23. 38 the heating coils of an electric clothes dryer can be counter - wound so that their magnetic fields cancel one another, greatly reducing the mutual inductance with the case of the dryer. s... | openstax_college_physics_2e-web_7zesafu | [
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happens if we try to shut off the current rapidly, perhaps in only 1. 0 ms? an emf, given by, will oppose the change. thus an emf will be induced given by. the positive sign means this large voltage is in the same direction as the current, opposing its decrease. such large emfs can cause arcs, damaging switching equipm... | openstax_college_physics_2e-web_7zesafu | [
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23. 9 • inductance 1033 figure 23. 40 through rapid switching of an inductor, 1. 5 v batteries can be used to induce emfs of several thousand volts. this voltage can be used to store charge in a capacitor for later use, such as in a camera flash attachment. it is possible to calculate for an inductor given its geometry... | openstax_college_physics_2e-web_7zesafu | [
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23. 7 calculating the self - inductance of a moderate size solenoid calculate the self - inductance of a 10. 0 cm long, 4. 00 cm diameter solenoid that has 200 coils. strategy this is a straightforward application of, since all quantities in the equation except are known. solution use the following expression for the s... | openstax_college_physics_2e-web_7zesafu | [
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23. 40 1034 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org the cross - sectional area in this example is, is given to be 200, and the length is 0. 100 m. we know the permeability of free space is. substituting these into the expression for gives discussion this... | openstax_college_physics_2e-web_7zesafu | [
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inductance of the device. it can be shown that the energy stored in an inductor is given by this expression is similar to that for the energy stored in a capacitor. example 23. 8 calculating the energy stored in the field of a solenoid how much energy is stored in the 0. 632 mh inductor of the preceding example when a ... | openstax_college_physics_2e-web_7zesafu | [
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23. 10 rl circuits learning objectives by the end of this section, you will be able to : • calculate the current in an rl circuit after a specified number of characteristic time steps. • calculate the characteristic time of an rl circuit. • sketch the current in an rl circuit over time. we know that the current through... | openstax_college_physics_2e-web_7zesafu | [
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capacitor ). the initial current is zero and approaches with a characteristic time constant for an rl circuit, given by 23. 44 23. 45 | openstax_college_physics_2e-web_7zesafu | [
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23. 46 1036 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org where has units of seconds, since. in the first period of time, the current rises from zero to, since. the current will go 0. 632 of the remainder in the next time. a well - known property of the expone... | openstax_college_physics_2e-web_7zesafu | [
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after the switch is closed, the current falls to 0. 368 of its initial value, since. in each successive time, the current falls to 0. 368 of the preceding value, and in a few multiples of, the current becomes very close to zero, as seen in the graph in figure 23. 42 ( c ). example 23. 9 calculating characteristic time ... | openstax_college_physics_2e-web_7zesafu | [
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changed, the current also changes, but the change in current lags the change in voltage in an rl circuit. in reactance, inductive and capacitive, we explore how an rl circuit behaves when a sinusoidal ac voltage is applied. | openstax_college_physics_2e-web_7zesafu | [
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23. 11 reactance, inductive and capacitive learning objectives by the end of this section, you will be able to : • sketch voltage and current versus time in simple inductive, capacitive, and resistive circuits. • calculate inductive and capacitive reactance. • calculate current and / or voltage in simple inductive, cap... | openstax_college_physics_2e-web_7zesafu | [
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zero just as the voltage reaches its positive peak to start another cycle. this behavior is summarized as follows : current lags behind voltage, since inductors oppose change in current. changing current induces a back emf. this is considered to be an effective resistance of the inductor to ac. the rms current through | openstax_college_physics_2e-web_7zesafu | [
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23. 50 ac voltage in an inductor when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one - fourth of a cycle, or by a phase angle. 1038 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org an inductor is given by a version of ohm ’ s... | openstax_college_physics_2e-web_7zesafu | [
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using the version of ohm ’ s law in equation, given the applied rms voltage is 120 v. for the first frequency, this yields similarly, at 10 khz, discussion the inductor reacts very differently at the two different frequencies. at the higher frequency, its reactance is large and the current is small, consistent with how... | openstax_college_physics_2e-web_7zesafu | [
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23. 11 • reactance, inductive and capacitive 1039 capacitors and capacitive reactance consider the capacitor connected directly to an ac voltage source as shown in figure 23. 44. the resistance of a circuit like this can be made so small that it has a negligible effect compared with the capacitor, and so we can assume ... | openstax_college_physics_2e-web_7zesafu | [
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. this is considered to be an effective resistance of the capacitor to ac, and so the rms current in the circuit containing only a capacitor is given by another version of ohm ’ s law to be where is the rms voltage and is defined ( as with, this expression for results from an analysis of the circuit using kirchhoff ’ s... | openstax_college_physics_2e-web_7zesafu | [
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23. 58 1040 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org example 23. 11 calculating capacitive reactance and then current ( a ) calculate the capacitive reactance of a 5. 00 µf capacitor when 60. 0 hz and 10. 0 khz ac voltages are applied. ( b ) what is the r... | openstax_college_physics_2e-web_7zesafu | [
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very high frequencies, the capacitor ’ s reactance tends to zero — it has a negligible reactance and does not impede the current ( it acts like a simple wire ). capacitors have the opposite effect on ac circuits that inductors have. resistors in an ac circuit just as a reminder, consider figure 23. 45, which shows an a... | openstax_college_physics_2e-web_7zesafu | [
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23. 12 rlc series ac circuits learning objectives by the end of this section, you will be able to : • calculate the impedance, phase angle, resonant frequency, power, power factor, voltage, and / or current in a rlc series circuit. • draw the circuit diagram for an rlc series circuit. • explain the significance of the ... | openstax_college_physics_2e-web_7zesafu | [
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, and is the impedance of the circuit. the units of impedance are ohms, and its effect on the circuit is as you might expect : the greater the impedance, the smaller the current. to get an expression for in terms of,, and, we will now examine how the voltages across the various components are related to the source volt... | openstax_college_physics_2e-web_7zesafu | [
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the impedance of an rlc series ac circuit. for circuits without a resistor, take ; for those without an inductor, take ; and for those without a capacitor, take. figure 23. 47 this graph shows the relationships of the voltages in an rlc circuit to the current. the voltages across the circuit elements add to equal the v... | openstax_college_physics_2e-web_7zesafu | [
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23. 12 • rlc series ac circuits 1043 example 23. 12 calculating impedance and current an rlc series circuit has a resistor, a 3. 00 mh inductor, and a capacitor. ( a ) find the circuit ’ s impedance at 60. 0 hz and 10. 0 khz, noting that these frequencies and the values for and are the same as in example 23. 10 and exa... | openstax_college_physics_2e-web_7zesafu | [
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function of the frequency of the driving voltage source? combining ohm ’ s law,, and the expression for impedance from gives the reactances vary with frequency, with large at high frequencies and large at low frequencies, as we have seen in three previous examples. at some intermediate frequency, the reactances will be... | openstax_college_physics_2e-web_7zesafu | [
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23. 69 1044 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org expression for by taking substituting the definitions of and, solving this expression for yields where is the resonant frequency of an rlc series circuit. this is also the natural frequency at which the... | openstax_college_physics_2e-web_7zesafu | [
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at that frequency is the same as if the resistor alone were in the circuit. solution for ( a ) entering the given values for and into the expression given for in yields 23. 70 23. 71 23. 72 23. 73 | openstax_college_physics_2e-web_7zesafu | [
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23. 12 • rlc series ac circuits 1045 discussion for ( a ) we see that the resonant frequency is between 60. 0 hz and 10. 0 khz, the two frequencies chosen in earlier examples. this was to be expected, since the capacitor dominated at the low frequency and the inductor dominated at the high frequency. their effects are ... | openstax_college_physics_2e-web_7zesafu | [
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resistor, a 3. 00 mh inductor, a capacitor, and a voltage source with a of 120 v : ( a ) calculate the power factor and phase angle for. ( b ) what is the average power at 50. 0 hz? ( c ) find the average power at the circuit ’ s resonant frequency. strategy and solution for ( a ) the power factor at 60. 0 hz is found ... | openstax_college_physics_2e-web_7zesafu | [
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23. 78 1046 23 • electromagnetic induction, ac circuits, and electrical technologies access for free at openstax. org discussion for ( a ) the phase angle is close to, consistent with the fact that the capacitor dominates the circuit at this low frequency ( a pure rc circuit has its voltage and current out of phase ). ... | openstax_college_physics_2e-web_7zesafu | [
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in the car spring ( analogous to no current, and energy stored in the electric field of a capacitor ). the amplitude of the wheels ’ motion is a maximum if the bumps in the road are hit at the resonant frequency. figure 23. 49 the forced but damped motion of the wheel on the car spring is analogous to an rlc series ac ... | openstax_college_physics_2e-web_7zesafu | [
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23. 12 • rlc series ac circuits 1047 analogy between an lc circuit and a mass on a spring. figure 23. 50 an lc circuit is analogous to a mass oscillating on a spring with no friction and no driving force. energy moves back and forth between the inductor and capacitor, just as it moves from kinetic to potential in the m... | openstax_college_physics_2e-web_7zesafu | [
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means of calculating the emf in a coil due to changing magnetic flux, given by henry the unit of inductance ; impedance the ac analogue to resistance in a dc circuit ; it is the combined effect of resistance, inductive reactance, and capacitive reactance in the form inductance a property of a device describing how effi... | openstax_college_physics_2e-web_7zesafu | [
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wiring system used at present for safety reasons, with live, neutral, and ground wires transformer a device that transforms voltages from one value to another using induction transformer equation the equation showing that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of ... | openstax_college_physics_2e-web_7zesafu | [
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##f — in motors, this is called back emf, since it opposes the emf input to the motor. 23. 7 transformers • transformers use induction to transform voltages from one value to another. • for a transformer, the voltages across the primary and secondary coils are related by where and are the voltages across primary and se... | openstax_college_physics_2e-web_7zesafu | [
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23. 9 inductance • inductance is the property of a device that tells how effectively it induces an emf in another device. • mutual inductance is the effect of two devices in inducing emfs in each other. • a change in current in one induces an emf in the second : where is defined to be the mutual inductance between the ... | openstax_college_physics_2e-web_7zesafu | [
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of the current is where is the final current. • the characteristic time constant is, where is the inductance and is the resistance. • in the first time constant, the current rises from zero to, and 0. 632 of the remainder in every subsequent time interval. • when the inductor is shorted through a resistor, current decr... | openstax_college_physics_2e-web_7zesafu | [
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