electrical-engineering-ai999x — offline, verified electrical engineering solver with step-by-step answers

Desktop app & command line · Compute in your browser · Install (Python) · Guides · Evaluation · AI999X on Hugging Face · Website · Support: Buy Me a Coffee

License: Apache-2.0 · Author: Ibnul Jaif Farabi (creator and engineer) · Organization: AI999X · Version 1.0.3

Field: Engineering · Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction

electrical-engineering-ai999x is an offline, deterministic Python solver that answers electrical engineering questions with verified results from 64 certified capabilities, gives 326 documented answers identically on Windows and Linux, and refuses rather than guesses when an answer cannot be verified.

electrical-engineering-ai999x is a compact, deterministic electrical engineering engine for Python. It reads a question in plain English (or a typed call), picks a certified electrical engineering capability, computes the answer exactly, checks it, and returns the result with its steps, units, LaTeX and assumptions — or an honest refusal that says what is missing. It runs fully offline on any CPU, needs no GPU, no API key and no internet, and is built to give zero wrong answers: when it is not sure, it refuses instead of guessing.

Run it your way. electrical-engineering-ai999x comes as the AI999X desktop app and as the command-line program electrical-engineering for Windows and Linux, runs in your browser as WebAssembly, and installs as a Python package. The desktop app, the command line and the browser run the same compiled Rust program on your own device: offline, no Python needed.

Get it

Way to run it	For	Get it
AI999X Electrical Engineering desktop app 1.2.0	Windows, Linux — this model in its own app: search, ask in words, forms, live figures, explanations, offline	Windows (x86-64) · Linux (x86-64)
AI999X desktop app 1.2.0	Windows, Linux — every AI999X model in one app: search, ask in words, forms, live figures, explanations, offline	Windows (x86-64) · Linux (x86-64)
Command line (electrical-engineering)	Windows, Linux — one program per model, offline, no Python	Windows (x86-64) · Linux (x86-64)
In your browser	any device — nothing to install	Compute on the model page
Python	Python 3.10+	pip install electrical-engineering-ai999x

Checksums: SHA256SUMS · every version: https://www.ai999x.com/downloads/desktop/latest/ · install guide: desktop & command line

Rust versions

Electrical Engineering also comes as native programs compiled from Rust, version 1.2.0 of the AI999X desktop app and command line: they run offline on your computer and need no Python. Each file is in this repository's rust/ folder, on the GitHub release v1.0.3 and on the website.

Program	System	File	Size	Download	Use
Desktop app (Electrical Engineering)	Windows x86-64	ai999x-electrical-engineering-1.2.0-windows-x86_64.zip	7.4 MB	Hub · GitHub · website	unzip, then double-click ai999x-electrical-engineering.exe (no installer)
Desktop app (Electrical Engineering)	Linux x86-64	ai999x-electrical-engineering-1.2.0-linux-x86_64.tar.gz	8.3 MB	Hub · GitHub · website	extract, then run ./ai999x-electrical-engineering (X11 or Wayland desktop)
Command line (electrical-engineering)	Windows x86-64	ai999x-electrical-engineering-cli-1.2.0-windows-x86_64.zip	3.1 MB	Hub · GitHub · website (all models)	unzip, then electrical-engineering.exe ask "<question>" or electrical-engineering.exe solve <capability> name=value
Command line (electrical-engineering)	Linux x86-64	ai999x-electrical-engineering-cli-1.2.0-linux-x86_64.tar.gz	3.1 MB	Hub · GitHub · website (all models)	extract, then ./electrical-engineering ask "<question>" or ./electrical-engineering solve <capability> name=value

The command-line archive holds electrical-engineering with a README of its commands and examples, the licence and the notice. Checksums: rust/SHA256SUMS (sha256sum -c SHA256SUMS).

Quick start

Desktop app

Download AI999X Electrical Engineering for your system (above), unpack it and start it; type a question in words or pick a capability, fill in the form and press Compute. Figures and an explanation of the answer appear beside it. The AI999X desktop app has the same, with Electrical Engineering among all AI999X models.

Linux, from a terminal:

curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/ai999x-electrical-engineering-1.2.0-linux-x86_64.tar.gz
curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS
sha256sum -c --ignore-missing SHA256SUMS
tar xzf ai999x-electrical-engineering-1.2.0-linux-x86_64.tar.gz
./ai999x-electrical-engineering-1.2.0-linux-x86_64/ai999x-electrical-engineering

Command line

Linux:

curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/ai999x-cli-1.2.0-linux-x86_64.tar.gz
curl -LO https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS
sha256sum -c --ignore-missing SHA256SUMS
mkdir -p ~/.local/share && tar xzf ai999x-cli-1.2.0-linux-x86_64.tar.gz -C ~/.local/share
echo 'export PATH="$HOME/.local/share/ai999x-cli-1.2.0-linux-x86_64:$PATH"' >> ~/.bashrc && source ~/.bashrc
electrical-engineering --version

Windows (PowerShell):

$F = "ai999x-cli-1.2.0-windows-x86_64.zip"
Invoke-WebRequest "https://www.ai999x.com/downloads/desktop/1.2.0/$F" -OutFile $F
Invoke-WebRequest "https://www.ai999x.com/downloads/desktop/1.2.0/SHA256SUMS" -OutFile SHA256SUMS
(Get-FileHash $F -Algorithm SHA256).Hash.ToLower() -eq ((Select-String -SimpleMatch $F SHA256SUMS).Line -split ' ')[0]
Expand-Archive $F -DestinationPath "$env:LOCALAPPDATA\AI999X" -Force
$D = "$env:LOCALAPPDATA\AI999X\ai999x-cli-1.2.0-windows-x86_64"; $env:Path += ";$D"
[Environment]::SetEnvironmentVariable("Path", [Environment]::GetEnvironmentVariable("Path", "User") + ";$D", "User")
electrical-engineering --version

Every command below was run as shown; the text under it is what the program printed.

Ask in words — Write the question as you would say it: the program reads the quantities and their units, picks the capability and answers.

$ electrical-engineering ask "Find the Thevenin equivalent between nodes 2 and 0 of the circuit: V1 1 0 12; R1 1 2 1000; R2 2 0 2000."
Read as: Thevenin equivalent of a DC circuit between two nodes
Vth = 8 V
Rth = 666.6666667 ohm
  by: Thevenin equivalent of a DC circuit between two nodes  (open-circuit voltage by modified nodal analysis; resistance by a 1 A test current with the independent sources set to zero)
  node_a = 2
  node_b = 0
  netlist = V1 1 0 12; R1 1 2 1000; R2 2 0 2000.
  assumes: both nodes in the circuit; no ideal voltage source directly across the terminals; a unique solution (no floating node)

What a capability needs — The equation or method, every input and output with its SI unit. Read this before solve: it tells you the input names.

$ electrical-engineering info thevenin_equivalent
Thevenin equivalent of a DC circuit between two nodes
  open-circuit voltage by modified nodal analysis; resistance by a 1 A test current with the independent sources set to zero
  in   netlist  elements separated by ';': R<name> <node> <node> <ohms>, V<name> <node+> <node-> <volts>, I<name> <node> <node> <amperes>; node 0 is ground (text) []
  in   node_a   the terminal node (the + side of the equivalent) (text) []
  in   node_b   the reference terminal node (text) []
  out  Vth      Thevenin (open-circuit) voltage, node a relative to node b [V]
  out  Rth      Thevenin resistance [ohm]

Solve — Inputs as name=value, each with any unit of the right kind. The answer lists every output, the method used, each input converted to SI, and the conditions the answer assumes.

$ electrical-engineering solve thevenin_equivalent node_a=2 node_b=0 "netlist=V1 1 0 12; R1 1 2 1000; R2 2 0 2000."
Vth = 8 V
Rth = 666.6666667 ohm
  by: Thevenin equivalent of a DC circuit between two nodes  (open-circuit voltage by modified nodal analysis; resistance by a 1 A test current with the independent sources set to zero)
  node_a = 2
  node_b = 0
  netlist = V1 1 0 12; R1 1 2 1000; R2 2 0 2000.
  assumes: both nodes in the circuit; no ideal voltage source directly across the terminals; a unique solution (no floating node)

Draw the figures — The live figures for your own inputs, written as SVG files into the folder given with --out (here the current folder); open them in any browser. Without --out the SVG text comes back as JSON.

$ electrical-engineering figures thevenin_equivalent node_a=2 node_b=0 "netlist=V1 1 0 12; R1 1 2 1000; R2 2 0 2000." --out .
[
  {
    "slug": "thevenin-equivalent-live-1",
    "title": "Thevenin (open-circuit) voltage, node a relat... as the number 0 in node_b (0) varies",
    "caption": "Thevenin (open-circuit) voltage, node a relat... as the number in node_b runs from 0 to 1, every other input as you entered it (2 solutions). Marked: your the number in node_b = 0 gives Vth = 8. Your inputs: node_a = 2, node_b = 0, netlist = V1 1 0 12; R1 1 2 1000; R....",
    "file": "./thevenin-equivalent-live-1.svg"
  },
  {
    "slug": "thevenin-equivalent-live-2",
    "title": "Thevenin (open-circuit) voltage, node a relat... as the number 1 in netlist (V1 1 0 12; R1 1 2 100...) varies",
    "caption": "Thevenin (open-circuit) voltage, node a relat... as the number in netlist runs from 1 to 5, every other input as you entered it (4 solutions). Values in this range where the inputs admit no answer (1 of 5) are left out. Marked: your the number in netlist = 1 gives Vth = 8. Your inputs: node_a = 2, node_b = 0, netlist = V1 1 0 12; R1 1 2 1000; R....",
    "file": "./thevenin-equivalent-live-2.svg"
  }
]

Many questions at once — One JSON request per line in, one JSON answer per line out, in order: for scripts, notebooks and agents (the program starts once). In PowerShell: Get-Content cases.jsonl | electrical-engineering batch

cases.jsonl:

{"key": "thevenin_equivalent", "inputs": {"node_a": "2", "node_b": "0", "netlist": "V1 1 0 12; R1 1 2 1000; R2 2 0 2000."}}
{"key": "gain_margin", "inputs": {"num": "[10]", "den": "[1, 6, 5, 0]"}}

$ electrical-engineering batch < cases.jsonl
{"outcome":"SOLVED","message":"","value":8.0,"unit":"V","solved_for":"Vth","values":[["Vth",8.0,"V"],["Rth",666.6666666666666,"ohm"]],"target":"Vth","phrase":"Thevenin (open-circuit) voltage, node a relative to node b","assumptions":["both nodes in the circuit","no ideal voltage source directly across the terminals","a unique solution (no floating node)"],"name":"Thevenin equivalent of a DC circuit between two nodes","equation":"open-circuit voltage by modified nodal analysis; resistance by a 1 A test current with the independent sources set to zero"}
{"outcome":"SOLVED","message":"","value":3.0,"unit":"","solved_for":"gain_margin","values":[["gain_margin",3.0,""],["gain_margin_db",9.542425094393248,""],["phase_crossover",2.23606797749979,"rad/s"]],"target":"gain_margin","phrase":"gain margin as a ratio","assumptions":["a proper G(s)","exactly one phase crossover with G negative real"],"name":"Gain margin and phase-crossover frequency","equation":"the phase crossover as the positive real root of Im(N(jw) conj D(jw)) with Re G < 0 (Aberth iteration, Newton-polished)"}

In your browser

Open Electrical Engineering on ai999x.com, choose a capability and press Compute: the model runs on your own device as WebAssembly; nothing is sent anywhere. Change any input (any unit of the right kind) and the answer, its explanation and the figures follow.

In your own page: electrical_engineering_ai999x.wasm and the loader ax-wasm.js (https://www.ai999x.com/compute/rust/ax-wasm.js).

Python

pip install electrical-engineering-ai999x

Worked examples in every form

The same worked example from the command line, from Python and in the browser. Each command-line output is what the program printed.

Balanced three-phase load (wye or delta)

Phase voltage, phase and line currents, real, reactive and apparent power and the power factor of a balanced load with impedance R + jX per phase.

Command line:

$ electrical-engineering solve three_phase_load connection=wye "VL=400 V" "R=8 ohm" "X=6 ohm"
phase_voltage = 230.9401077 V
phase_current = 23.09401077 A
line_current = 23.09401077 A
P = 12800 W
Q = 9600 W
S = 16000 W
power_factor = 0.8
  by: Balanced three-phase load (wye or delta)  (wye: V_ph = V_L/sqrt(3), I_L = I_ph; delta: V_ph = V_L, I_L = sqrt(3) I_ph; P = 3 I_ph^2 R)
  VL = 400 V
  R = 8 ohm
  X = 6 ohm
  connection = wye
  assumes: balanced load and supply; R >= 0

Python:

import electrical_engineering_ai999x as m

a = m.solve("three_phase_load", connection="wye", VL="400 V", R="8 ohm", X="6 ohm")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

What this means: This calculation determines the electrical characteristics of a balanced three-phase load connected in a wye configuration. Using a line-to-line voltage of 400 V and per-phase impedance defined by resistance 8 ohm and reactance 6 ohm, it computes the phase voltage as 230.94 V, phase current as 23.094 A, and line current as 23.094 A. The resulting total real power is 12800 W, reactive power is 9600 W, apparent power is 16000 W, and the power factor is 0.8. These values indicate how much useful work is performed versus how much energy oscillates between source and load.

Complex, real, reactive and apparent power from voltage and current phasors

S = V I* for rms phasors: real power P, reactive power Q, apparent power |S|, the power factor and whether it lags or leads.

Command line:

$ electrical-engineering solve complex_power "V=230 V" V_phase=0 "I=10 A" I_phase=-30
P = 1991.858429 W
Q = 1150 W
S = 2300 W
power_factor = 0.8660254038
nature = lagging
  by: Complex, real, reactive and apparent power from voltage and current phasors  (S = V I* (complex conjugate of the current))
  V = 230 V
  V_phase = 0
  I = 10 A
  I_phase = -30
  assumes: rms phasors; sinusoidal steady state

Python:

import electrical_engineering_ai999x as m

a = m.solve("complex_power", V="230 V", V_phase="0", I="10 A", I_phase="-30")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

Energy stored in an inductor

The magnetic energy L I^2/2 and the flux linkage L I of an inductor carrying current I.

Command line:

$ electrical-engineering solve inductor_energy "L=0.05 H" "I=2 A"
energy = 0.1 J
flux_linkage = 0.1
  by: Energy stored in an inductor  (W = L I^2 / 2)
  L = 0.05 H
  I = 2 A
  assumes: a linear inductor (no saturation)

Python:

import electrical_engineering_ai999x as m

a = m.solve("inductor_energy", L="0.05 H", I="2 A")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

What this means: This calculation determines the magnetic energy stored in an inductor and its flux linkage based on the given inductance of 0.05 H and current of 2 A. The resulting energy of 0.1 J represents the work done to establish the magnetic field, while the flux linkage of 0.1 indicates the total magnetic flux coupled with the coil turns. These values are critical for analyzing circuit transients and power conversion efficiency.

First-order RC filter: cutoff, gain and phase

The cutoff frequency 1/(2 pi R C) of an RC low-pass or high-pass filter and its gain (ratio and dB) and phase at a frequency.

Command line:

$ electrical-engineering solve rc_filter "R=1000 ohm" "C=1e-07 F" "f=2000 Hz" filter=lowpass
fc = 1591.549431 Hz
gain = 0.6226769923
gain_db = -4.11474362
phase_deg = -51.48811275
  by: First-order RC filter: cutoff, gain and phase  (H = 1/(1 + j f/fc) (low-pass) or (j f/fc)/(1 + j f/fc) (high-pass))
  R = 1000 ohm
  C = 1e-07 F
  f = 2000 Hz
  filter = lowpass
  assumes: unloaded output; R, C, f > 0

Python:

import electrical_engineering_ai999x as m

a = m.solve("rc_filter", R="1000 ohm", C="1e-07 F", f="2000 Hz", filter="lowpass")
print(a.values or (a.value, a.unit))

Browser: open this capability on the model page and press Compute in your browser.

What this means: This calculation determines the cutoff frequency, magnitude gain, decibel gain, and phase shift for a first-order RC filter. Using resistance 1000 ohm, capacitance 1e-07 F, and signal frequency 2000 Hz, it finds that the cutoff frequency is 1591.55 Hz. The resulting voltage gain ratio is 0.622677, which corresponds to -4.11474 in decibels, with a phase shift of -51.4881 degrees between output and input.

Documentation

• Rust user guide — the command line, every capability with a command and what it printed: PDF · Markdown
• Python guide — every capability with a Python example: PDF · Markdown
• Desktop app & command line — downloads, install, ask and search, figures, offline use, checksums: https://www.ai999x.com/desktop-cli/
• Model page — compute in your browser, every capability explained: https://www.ai999x.com/models/electrical-engineering-ai999x/

Highlights

• Verified, not generated. Every answer is computed by a certified electrical engineering capability and checked (substituted back, dimension-checked or compared with an independent computation) before it is returned.
• Zero wrong answers by design. Seven explicit outcomes — SOLVED, NEEDS_INPUT, AMBIGUOUS, INVALID_INPUT, OUT_OF_SCOPE, UNRECOGNIZED_FORMAT, INTERNAL_ERROR — never a silent guess. Every one of its 326 documented answers is reproduced exactly on every tested platform.
• Plain-English questions and a guaranteed typed interface. ask() reads documented question forms; solve(capability_id, **inputs) always solves a supported task with valid inputs.
• Explains itself. Steps, formulas in LaTeX, units, assumptions and the model used, ready for notebooks, tutoring apps and homework checkers.
• Native and in the browser. Every capability also computes natively in Rust: the desktop app and the electrical-engineering command line for Windows and Linux, and WebAssembly on the model page — no Python, no network.
• Small and portable. Pure Python (sympy, mpmath); identical answers on Windows and Linux (Python 3.10, 3.11, 3.12, 3.13, 3.14).
• Coverage: DC and AC circuits, transients, phasors and power, operational amplifiers, diodes and transistors, digital logic, and control systems (transfer functions, stability, Bode).

Model overview

Property	Value
Package	electrical-engineering-ai999x 1.0.3 (import electrical_engineering_ai999x)
Type	Deterministic neuro-symbolic electrical engineering engine (rule-based reading + certified symbolic capabilities)
Capabilities	64 certified procedures
Knowledge pack	version 1.0.0
Golden answers	326 documented answers, identical on every tested platform
Platforms tested	Windows (Python 3.13), Linux x86-64 (Python 3.10, 3.11, 3.12, 3.13, 3.14)
Runtime	CPU only, offline; no GPU, no network, no API key
License	Apache-2.0
Creator / engineer	Ibnul Jaif Farabi
Organization	AI999X

Python quick start

pip install electrical-engineering-ai999x
# or straight from this repository:
pip install https://huggingface.co/AI999X/electrical-engineering-ai999x/resolve/main/dist/electrical_engineering_ai999x-1.0.3-py3-none-any.whl

import electrical_engineering_ai999x as electrical_engineering

electrical_engineering.ask("Find the Thevenin equivalent between nodes 2 and 0 of the circuit: V1 1 0 12; R1 1 2 1000; R2 2 0 2000.").show()
# -> SOLVED — Vth = 8, Rth = 666.667  (thevenin_equivalent)
electrical_engineering.ask("Find the gain margin of G(s) = 10/(s(s+1)(s+5)).").show()
# -> SOLVED — gain_margin = 3, gain_margin_db = 9.54243, phase_crossover = 2.23607  (gain_margin)
electrical_engineering.ask("Simplify F(A,B,C) = \u03a3m(0, 1, 2, 5, 6, 7).").show()
# -> SOLVED — minimal_sop = A'·B' + A·C + B·C', terms = 3, literals = 6, variables = A, B, C  (minterms_to_sop)
electrical_engineering.ask("A load draws 10 kW at a power factor of 0.7 from a 230 V, 50 Hz supply. What capacitance corrects the power factor to 0.95?").show()
# -> SOLVED — C = 0.000416101, C_uF = 416.101, Qc = 6915.2, Q_initial = 10202  (power_factor_correction)
electrical_engineering.solve("series_rlc_impedance", R="100 ohm", L="50 mH", C="10 uF", f="1 kHz").show()
# -> SOLVED — impedance = 314.562, phase_deg = 71.4639, real = 100, imag = 298.244  (series_rlc_impedance)
electrical_engineering.ask("Who created you?").message
# -> electrical-engineering-ai999x was created and engineered by Ibnul Jaif Farabi at AI999X.

The Python package also installs a Python command, electrical-engineering-ai999x "<question>"; for the native program use electrical-engineering (above). The outputs above were produced by running this exact code on electrical-engineering-ai999x 1.0.3.

Find the right capability, and draw it

electrical_engineering.search() finds which certified capability a question is about — across every AI999X model, so a question for another model points you to it. It runs ai999x-encoder, AI999X's own capability encoder (4.7M parameters, a 4.9 MB ONNX model, offline; the root model.safetensors of this repository): pip install "electrical-engineering-ai999x[search]". ask(question, suggest=True) adds the same pointers to a question it does not answer; an answer itself never changes.

import electrical_engineering_ai999x as electrical_engineering

electrical_engineering.search("Solve x^2 - 5x + 6 = 0", k=2)
# -> Roots of a quadratic equation (math-foundations-ai999x, 0.63); Roots of a cubic equation (math-foundations-ai999x, 0.59)

How every answer is verified

1. Reading — the question is turned into typed quantities (value, unit, kind, role) and one asked quantity; every stated number must be used or the question is refused.
2. Planning — only certified capabilities may answer; a capability applies only under the conditions the wording states (for example a pendulum, a liquid at rest, boiling).
3. Computing — exact symbolic or high-precision numeric evaluation.
4. Checking — dimensions, substitution back into the defining equation, and agreement between independent readings; any disagreement becomes a refusal, never a number.

Capabilities are certified before they ship: each must reproduce hand-worked reference cases, reject a deliberately wrong variant (a control), and leave every benchmark answer unchanged.

Python worked examples, with their steps

Each question was put to electrical-engineering-ai999x; the answer is the one it returned, with the steps it took.

Thevenin equivalent of a DC circuit between two nodes · DC circuits

Find the Thevenin equivalent between nodes 2 and 0 of the circuit: V1 1 0 12; R1 1 2 1000; R2 2 0 2000.

→ Vth = 8 V, Rth = 666.6666667 ohm

Steps

• Thevenin equivalent of a DC circuit between two nodes: node_a = 2, node_b = 0, netlist = V1 1 0 12; R1 1 2 1000; R2 2 0 2000. → Vth = 8 V, Rth = 666.6666667 ohm

Gain margin and phase-crossover frequency · Control systems

Find the gain margin of G(s) = 10/(s(s+1)(s+5)).

→ gain_margin = 3, gain_margin_db = 9.542425094, phase_crossover = 2.236067977 rad/s

Steps

• Gain margin and phase-crossover frequency: num = [10], den = [1, 6, 5, 0] → gain_margin = 3, gain_margin_db = 9.542425094, phase_crossover = 2.236067977 rad/s

Minimal sum of products from minterms (with don't-cares) · Digital logic

Simplify F(A,B,C) = Σm(0, 1, 2, 5, 6, 7).

→ minimal_sop = A'·B' + A·C + B·C', terms = 3, literals = 6, variables = A, B, C

Steps

• Minimal sum of products from minterms (with don't-cares): minterms = [0, 1, 2, 5, 6, 7], variables = 3 → minimal_sop = A'·B' + A·C + B·C', terms = 3, literals = 6, variables = A, B, C

Power-factor correction capacitor · AC circuits

A load draws 10 kW at a power factor of 0.7 from a 230 V, 50 Hz supply. What capacitance corrects the power factor to 0.95?

→ C = 0.000416101396 F, C_uF = 416.101396, Qc = 6915.19956 W, Q_initial = 10202.04061 W, Q_final = 3286.841052 W

Steps

• Power-factor correction capacitor: P = 10000 W, V = 230 V, f = 50 Hz, pf_initial = 0.7, pf_target = 0.95 → C = 0.000416101396 F, C_uF = 416.101396, Qc = 6915.19956 W, Q_initial = 10202.04061 W, Q_final = 3286.841052 W

Impedance of a series RLC circuit · AC circuits

m.solve("series_rlc_impedance", R="100 ohm", L="50 mH", C="10 uF", f="1 kHz")

→ impedance = 314.5621512 ohm, phase_deg = 71.46389381, real = 100 ohm, imag = 298.243771 ohm, XL = 314.1592654 ohm, XC = 15.91549431 ohm

Steps

• Impedance of a series RLC circuit: R = 100 ohm, L = 50 mH, C = 10 uF, f = 1 kHz → impedance = 314.5621512 ohm, phase_deg = 71.46389381 ohm, real = 100 ohm, imag = 298.243771 ohm, XL = 314.1592654 ohm, XC = 15.91549431 ohm

DC operating point of a voltage-divider biased BJT · Diodes and transistors

A voltage-divider biased BJT has VCC = 12 V, R1 = 10 kohm, R2 = 2.2 kohm, RC = 3.6 kohm, RE = 1 kohm, beta = 100 and VBE = 0.7 V. Find the collector current.

→ IC = 0.001424015309 A, IC_mA = 1.424015309, IB = 1.424015309e-05 A, IE = 0.001438255462 A, VB = 2.138255462 V, VE = 1.438255462 V, VC = 6.873544889 V, VCE = 5.435289428 V

Steps

• DC operating point of a voltage-divider biased BJT: VCC = 12 V, VBE = 0.7 V, R1 = 10000 ohm, R2 = 2200 ohm, RC = 3600 ohm, RE = 1000 ohm, beta = 100 → IC = 0.001424015309 A, IC_mA = 1.424015309, IB = 1.424015309e-05 A, IE = 0.001438255462 A, VB = 2.138255462 V, VE = 1.438255462 V, VC = 6.873544889 V, VCE = 5.435289428 V

Figures

Every point was computed by electrical-engineering-ai999x.

Series RLC step response: under-, critically and over-damped

Capacitor voltage of a series RLC circuit switched onto V = 12 V (L = 0.1 H, C = 0.0001 F) for three resistances, 121 instants each computed by the package: R = 10 Ω: ζ = 0.158114, underdamped; R = 63.2456 Ω: ζ = 1, critically damped; R = 150 Ω: ζ = 2.37171, overdamped. Marked: t = 0.005 s, vC = 10.4144 V (R = 10 Ω).

Bode magnitude and gain margin of a third-order loop

Bode magnitude of G(s) = 10 / (s^3 + 6s^2 + 5s), 101 frequencies from 0.01 to 100 rad/s computed by the package. At the phase crossover ω = 2.23607 rad/s the gain is -9.54243 dB, so the gain margin returned by the package is 9.54243 dB (a factor 3); marked: ω = 2.23607 rad/s, |G| = -9.54243 dB.

Phasors and their sum on a polar chart

Three phasors 3∠0°, 4∠90° and 2∠210° on a polar chart (each converted to rectangular form by the package; rings every 1 unit of amplitude) and their sum returned by the package: 3.25695 ∠ 67.0887° = 1.26795 + 3j. Marked: the tip of the sum, real = 1.26795, imaginary = 3.

Power triangle: real, reactive and apparent power

Power triangle of a load with V = 230 V ∠ 0° and I = 10 A ∠ -30°, from the complex power the package returned: real power P = 1991.86 W, reactive power Q = 1150 var (lagging), apparent power S = 2300 VA, power factor 0.866025. Marked: the tip of S.

Mesh analysis as matrices: resistances, sources, currents

Mesh analysis of a three-loop circuit as matrices: the mesh-resistance matrix R (self resistances on the diagonal, shared resistances negative off it) and the loop EMFs E are the stated circuit (R I = E); the mesh currents I are the solution returned by the package: I1 = 0.864914 A, I2 = 0.320943 A, I3 = -0.157752 A (a negative current flows against the assumed direction). Each panel is shaded by its own largest magnitude; negative values in the second colour.

Capabilities

64 certified procedures. A few of them:

• Procedures: Analog-to-digital conversion: output code and resolution; Balanced three-phase load (wye or delta); Binary to Gray code and Gray code to binary; Closed-loop poles with unity negative feedback; Complex, real, reactive and apparent power from voltage and current phasors; Controllability and observability of a single-input single-output system; Current divider; DC operating point of a voltage-divider biased BJT; Delta-to-wye (Pi-to-T) resistor transformation; Difference amplifier output (four-resistor op-amp circuit); Energy stored in an inductor; Equivalence of two Boolean expressions; Equivalent capacitance of capacitors in parallel; Equivalent capacitance of capacitors in series; Equivalent inductance of inductors in parallel; Equivalent inductance of inductors in series; Equivalent resistance of a series-parallel resistor network; Equivalent resistance of resistors in parallel; Equivalent resistance of resistors in series; Evaluate a Boolean expression; First-order (RC or RL) transient response; First-order RC filter: cutoff, gain and phase; Frequency response (Bode magnitude and phase) at one frequency; Gain margin and phase-crossover frequency …

electrical_engineering_ai999x.templates() lists every question form ask() reads; the capability guide (PDF, every example executed) is included in this repository.

All 64 formulas

Show every formula, by topic

AC circuits / AC power

Complex, real, reactive and apparent power from voltage and current phasors

$$S=V{I}^{\ast }=P+jQ,\mathrm{p}\mathrm{f}=\frac{P}{\mathrm{\mid }S\mathrm{\mid }}S\; =\; V\; I^*\; =\; P\; +\; jQ,\backslash quad\; \backslash mathrm\{pf\}\; =\; \backslash frac\{P\}\{\backslash vert\; S\backslash vert\; \}$$

Power-factor correction capacitor

$$C=\frac{P(\tan {\varphi }_1-\tan {\varphi }_2)}{2\pi f{V}^2}C\; =\; \backslash frac\{P(\backslash tan\backslash phi\_1\; -\; \backslash tan\backslash phi\_2)\}\{2\backslash pi\; f\; V^2\}$$

AC circuits / energy storage

Energy stored in an inductor

$$W=\frac{1}{2}L{I}^{2}W\; =\; \backslash tfrac\{1\}\{2\}LI^2$$

AC circuits / filters

First-order RC filter: cutoff, gain and phase

$$f_c=\frac{1}{2\pi RC},H_{LP}=\frac{1}{1+jf\mathrm{/}{f}_c}f\_c\; =\; \backslash frac\{1\}\{2\backslash pi\; RC\},\backslash quad\; H\_\{LP\}\; =\; \backslash frac\{1\}\{1\; +\; j\; f/f\_c\}$$

AC circuits / impedance

Impedance of a parallel RLC circuit

$$\frac{1}{Z}=\frac{1}{R}+j(\omega C-\frac{1}{\omega L})\backslash frac\{1\}\{Z\}\; =\; \backslash frac\{1\}\{R\}\; +\; j\backslash left(\backslash omega\; C\; -\; \backslash frac\{1\}\{\backslash omega\; L\}\backslash right)$$

Impedance of a series RLC circuit

$$Z=R+j(\omega L-\frac{1}{\omega C})Z\; =\; R\; +\; j\backslash left(\backslash omega\; L\; -\; \backslash frac\{1\}\{\backslash omega\; C\}\backslash right)$$

AC circuits / phasors

Phasor from polar to rectangular form

$$M\mathrm{\angle }\theta =M\cos \theta +jM\sin \theta M\backslash angle\backslash theta\; =\; M\backslash cos\backslash theta\; +\; jM\backslash sin\backslash theta$$

Phasor from rectangular to polar form

$$x+jy=\sqrt{x^2+y^2}\mathrm{\angle }\mathrm{atan2}(y,x)x\; +\; jy\; =\; \backslash sqrt\{x^2+y^2\}\backslash ,\backslash angle\backslash ,\backslash operatorname\{atan2\}(y,\; x)$$

Sum of sinusoids by phasor addition

$$\sum _k{A}_k\mathrm{\angle }{\varphi }_k=\sum _k{A}_k{e}^{j{\varphi }_k}\backslash sum\_k\; A\_k\backslash angle\backslash phi\_k\; =\; \backslash sum\_k\; A\_k\; e^\{j\backslash phi\_k\}$$

AC circuits / resonance

Resonance, Q factor and bandwidth of a parallel RLC circuit

$$f_0=\frac{1}{2\pi \sqrt{LC}},Q=R\sqrt{\frac{C}{L}}f\_0\; =\; \backslash frac\{1\}\{2\backslash pi\backslash sqrt\{LC\}\},\backslash \; Q\; =\; R\backslash sqrt\{\backslash frac\{C\}\{L\}\}$$

Resonance, Q factor and bandwidth of a series RLC circuit

$$f_0=\frac{1}{2\pi \sqrt{LC}},Q=\frac{1}{R}\sqrt{\frac{L}{C}}f\_0\; =\; \backslash frac\{1\}\{2\backslash pi\backslash sqrt\{LC\}\},\backslash \; Q\; =\; \backslash frac\{1\}\{R\}\backslash sqrt\{\backslash frac\{L\}\{C\}\}$$

AC circuits / three-phase power

Balanced three-phase load (wye or delta)

$$P=\sqrt{3}{V}_L{I}_L\cos \varphi P\; =\; \backslash sqrt\{3\}\backslash ,V\_L\; I\_L\; \backslash cos\backslash phi$$

AC circuits / transformers

Ideal transformer: voltages, currents and reflected resistance

$$\frac{V_s}{V_p}=\frac{N_s}{N_p},R_{in}=R_L{\left(\frac{N_p}{N_s}\right)}^2\backslash frac\{V\_s\}\{V\_p\}\; =\; \backslash frac\{N\_s\}\{N\_p\},\backslash quad\; R\_\{in\}\; =\; R\_L\backslash left(\backslash frac\{N\_p\}\{N\_s\}\backslash right)^2$$

AC circuits / waveforms

RMS and average value of a periodic waveform

$$V_{rms}=\sqrt{\frac{1}{T}{\int }_0^T{v}^{2}dt}V\_\{rms\}\; =\; \backslash sqrt\{\backslash frac\{1\}\{T\}\backslash int\_0^T\; v^2\backslash ,dt\}$$

DC circuits / Thevenin and Norton equivalents

Maximum power transfer

$$P_{max}=\frac{V_{th}^2}{4R_{th}}P\_\{max\}\; =\; \backslash frac\{V\_\{th\}^2\}\{4R\_\{th\}\}$$

Norton equivalent of a DC circuit between two nodes

$$I_N=\frac{V_{th}}{R_{th}},R_N=R_{th}I\_N\; =\; \backslash frac\{V\_\{th\}\}\{R\_\{th\}\},\backslash quad\; R\_N\; =\; R\_\{th\}$$

Thevenin equivalent of a DC circuit between two nodes

$$V_{th}=v_a-v_b{\mid }_{open},R_{th}=\frac{v_a-v_b}{1\mathrm{A}}{\mid }_{sourcesoff}V\_\{th\}\; =\; v\_a\; -\; v\_b\backslash big\backslash vert\; \_\{open\},\backslash quad\; R\_\{th\}\; =\; \backslash frac\{v\_a\; -\; v\_b\}\{1\backslash ,\backslash mathrm\{A\}\}\backslash big\backslash vert\; \_\{sources\backslash \; off\}$$

DC circuits / bridges

Wheatstone bridge output

$$V_{out}=V_s(\frac{R_2}{R_1+R_2}-\frac{R_4}{R_3+R_4})V\_\{out\}\; =\; V\_s\backslash left(\backslash frac\{R\_2\}\{R\_1+R\_2\}\; -\; \backslash frac\{R\_4\}\{R\_3+R\_4\}\backslash right)$$

DC circuits / dividers

Current divider

$$I_1=I\frac{R_2}{R_1+R_2}I\_1\; =\; I\backslash frac\{R\_2\}\{R\_1\; +\; R\_2\}$$

Voltage divider

$$V_{out}=V_{in}\frac{R_2}{R_1+R_2}V\_\{out\}\; =\; V\_\{in\}\backslash frac\{R\_2\}\{R\_1\; +\; R\_2\}$$

DC circuits / mesh and nodal analysis

Mesh currents from the mesh equations (Kirchhoff's voltage law)

$$\mathbf{R}\mathbf{i}=\mathbf{v}\backslash mathbf\{R\}\backslash ,\backslash mathbf\{i\}\; =\; \backslash mathbf\{v\}$$

Node voltages from the nodal equations (Kirchhoff's current law)

$$\mathbf{G}\mathbf{v}=\mathbf{i}\backslash mathbf\{G\}\backslash ,\backslash mathbf\{v\}\; =\; \backslash mathbf\{i\}$$

Node voltages of a DC resistive circuit from its netlist

DC circuits / network transformations

Delta-to-wye (Pi-to-T) resistor transformation

$$R_a=\frac{R_{ab}{R}_{ca}}{R_{ab}+R_{bc}+R_{ca}}R\_a\; =\; \backslash frac\{R\_\{ab\}R\_\{ca\}\}\{R\_\{ab\}+R\_\{bc\}+R\_\{ca\}\}$$

Wye-to-delta (T-to-Pi) resistor transformation

$$R_{ab}=\frac{R_a{R}_b+R_b{R}_c+R_c{R}_a}{R_c}R\_\{ab\}\; =\; \backslash frac\{R\_aR\_b\; +\; R\_bR\_c\; +\; R\_cR\_a\}\{R\_c\}$$

DC circuits / series and parallel combinations

Equivalent capacitance of capacitors in parallel

$$C_{eq}=\sum _i{C}_{i}C\_\{eq\}\; =\; \backslash sum\_i\; C\_i$$

Equivalent capacitance of capacitors in series

$$\frac{1}{C_{eq}}=\sum _i\frac{1}{C_i}\backslash frac\{1\}\{C\_\{eq\}\}\; =\; \backslash sum\_i\; \backslash frac\{1\}\{C\_i\}$$

Equivalent inductance of inductors in parallel

$$\frac{1}{L_{eq}}=\sum _i\frac{1}{L_i}\backslash frac\{1\}\{L\_\{eq\}\}\; =\; \backslash sum\_i\; \backslash frac\{1\}\{L\_i\}$$

Equivalent inductance of inductors in series

$$L_{eq}=\sum _i{L}_{i}L\_\{eq\}\; =\; \backslash sum\_i\; L\_i$$

Equivalent resistance of a series-parallel resistor network

$$R_s=R_1+R_2,R_p={(\frac{1}{R_1}+\frac{1}{R_2})}^{-1}R\_s\; =\; R\_1\; +\; R\_2,\backslash quad\; R\_p\; =\; \backslash left(\backslash frac\{1\}\{R\_1\}\; +\; \backslash frac\{1\}\{R\_2\}\backslash right)^\{-1\}$$

Equivalent resistance of resistors in parallel

$$\frac{1}{R_{eq}}=\sum _i\frac{1}{R_i}\backslash frac\{1\}\{R\_\{eq\}\}\; =\; \backslash sum\_i\; \backslash frac\{1\}\{R\_i\}$$

Equivalent resistance of resistors in series

$$R_{eq}=\sum _i{R}_{i}R\_\{eq\}\; =\; \backslash sum\_i\; R\_i$$

Control systems / compensation

Maximum phase lead of a lead compensator

$${\varphi }_{max}={\sin }^{-1}\frac{p-z}{p+z},{\omega }_m=\sqrt{zp}\backslash phi\_\{max\}\; =\; \backslash sin^\{-1\}\backslash frac\{p\; -\; z\}\{p\; +\; z\},\backslash \; \backslash omega\_m\; =\; \backslash sqrt\{zp\}$$

Control systems / electromechanical systems

Steady-state speed and current of a permanent-magnet DC motor

$$\omega =\frac{K_{t}V-RT}{K_t{K}_e+Rb}\backslash omega\; =\; \backslash frac\{K\_tV\; -\; RT\}\{K\_tK\_e\; +\; Rb\}$$

Control systems / frequency response

Frequency response (Bode magnitude and phase) at one frequency

$$G(j\omega )=\frac{N(j\omega )}{D(j\omega )},20{\log }_{10}\mathrm{\mid }G(j\omega )\mathrm{\mid }G(j\backslash omega)\; =\; \backslash frac\{N(j\backslash omega)\}\{D(j\backslash omega)\},\backslash quad\; 20\backslash log\_\{10\}\backslash vert\; G(j\backslash omega)\backslash vert$$

Gain margin and phase-crossover frequency

$$\mathrm{\angle }G(j{\omega }_{pc})=-{180}^{\circ },\mathrm{G}\mathrm{M}=\frac{1}{\mathrm{\mid }G(j{\omega }_{pc})\mathrm{\mid }}\backslash angle\; G(j\backslash omega\_\{pc\})\; =\; -180^\backslash circ,\backslash quad\; \backslash mathrm\{GM\}\; =\; \backslash frac\{1\}\{\backslash vert\; G(j\backslash omega\_\{pc\})\backslash vert\; \}$$

Phase margin and gain-crossover frequency

$$\mathrm{\mid }G(j{\omega }_c)\mathrm{\mid }=1,\mathrm{P}\mathrm{M}={180}^{\circ }+\mathrm{\angle }G(j{\omega }_c)\backslash vert\; G(j\backslash omega\_c)\backslash vert\; =\; 1,\backslash quad\; \backslash mathrm\{PM\}\; =\; 180^\backslash circ\; +\; \backslash angle\; G(j\backslash omega\_c)$$

Control systems / stability

Closed-loop poles with unity negative feedback

$$1+KG(s)=0⟺\mathrm{d}\mathrm{e}\mathrm{n}(s)+K\mathrm{n}\mathrm{u}\mathrm{m}(s)=01\; +\; K\backslash ,G(s)\; =\; 0\; \backslash iff\; \backslash mathrm\{den\}(s)\; +\; K\backslash ,\backslash mathrm\{num\}(s)\; =\; 0$$

Routh-Hurwitz stability test

$$b_i=\frac{a_1{a}_{0,i+1}-a_0{a}_{1,i+1}}{a_1}b\_i\; =\; \backslash frac\{a\_\{1\}\backslash ,a\_\{0,i+1\}\; -\; a\_\{0\}\backslash ,a\_\{1,i+1\}\}\{a\_\{1\}\}$$

Control systems / state space

Controllability and observability of a single-input single-output system

$$\mathcal{C}=[BAB\cdots A^{n-1}B],\mathcal{O}=[C;CA;\cdots ;C{A}^{n-1}]\backslash mathcal\{C\}\; =\; [B\backslash \; AB\backslash \; \backslash cdots\backslash \; A^\{n-1\}B],\backslash \; \backslash mathcal\{O\}\; =\; [C;\backslash \; CA;\backslash \; \backslash cdots;\backslash \; CA^\{n-1\}]$$

Transfer function of a single-input single-output state-space model

$$G(s)=C(sI-A{)}^{-1}B+DG(s)\; =\; C(sI\; -\; A)^\{-1\}B\; +\; D$$

Control systems / steady-state accuracy

Steady-state error of a unity-feedback system

$$e_{ss}=\underset{s\to 0}{\lim }\frac{sR(s)}{1+G(s)}e\_\{ss\}\; =\; \backslash lim\_\{s\backslash to\; 0\}\; \backslash frac\{s\backslash ,R(s)\}\{1\; +\; G(s)\}$$

Control systems / time response

Step-response specifications of a standard second-order system

$$M_p=e^{-\zeta \pi \mathrm{/}\sqrt{1-{\zeta }^2}},t_p=\frac{\pi }{{\omega }_n\sqrt{1-{\zeta }^2}}M\_p\; =\; e^\{-\backslash zeta\backslash pi/\backslash sqrt\{1-\backslash zeta^2\}\},\backslash quad\; t\_p\; =\; \backslash frac\{\backslash pi\}\{\backslash omega\_n\backslash sqrt\{1-\backslash zeta^2\}\}$$

Digital logic / Boolean algebra

Equivalence of two Boolean expressions

$$F_1\equiv F_2⟺F_1\oplus F_2=0F\_1\; \backslash equiv\; F\_2\; \backslash iff\; F\_1\; \backslash oplus\; F\_2\; =\; 0$$

Evaluate a Boolean expression

$$F(A,B,\dots )\in \{0,1\}F(A,\; B,\; \backslash dots)\; \backslash in\; \backslash \{0,\; 1\backslash \}$$

Digital logic / data conversion

Analog-to-digital conversion: output code and resolution

$$\mathrm{c}\mathrm{o}\mathrm{d}\mathrm{e}=\lfloor \frac{V_{in}}{V_{ref}\mathrm{/}{2}^n}\rfloor \backslash mathrm\{code\}\; =\; \backslash left\backslash lfloor\; \backslash frac\{V\_\{in\}\}\{V\_\{ref\}/2^n\}\; \backslash right\backslash rfloor$$

Digital logic / minimization

Minimal sum of products from minterms (with don't-cares)

$$F=\sum m(\dots )+\sum d(\dots )F\; =\; \backslash sum\; m(\backslash dots)\; +\; \backslash sum\; d(\backslash dots)$$

Truth table and minimal sum of products of a Boolean expression

$$F=\sum m(\dots )F\; =\; \backslash sum\; m(\backslash dots)$$

Digital logic / number systems

Binary to Gray code and Gray code to binary

$$g=b\oplus (b\gg 1)g\; =\; b\; \backslash oplus\; (b\; \backslash gg\; 1)$$

Number base conversion (binary, octal, decimal, hexadecimal)

$$N=\sum _i{d}_i{b}^{i}N\; =\; \backslash sum\_i\; d\_i\backslash ,\; b^i$$

Two's complement representation of a signed integer

$$x_{2c}=x{2}^{n}x\_\{2c\}\; =\; x\; \backslash bmod\; 2^n$$

Value of a two's complement bit pattern

Diodes and transistors / BJT biasing

DC operating point of a voltage-divider biased BJT

$$I_B=\frac{V_{TH}-V_{BE}}{R_{TH}+(\beta +1)R_E},V_{TH}=V_{CC}\frac{R_2}{R_1+R_2}I\_B\; =\; \backslash frac\{V\_\{TH\}\; -\; V\_\{BE\}\}\{R\_\{TH\}\; +\; (\backslash beta+1)R\_E\},\backslash quad\; V\_\{TH\}\; =\; V\_\{CC\}\backslash frac\{R\_2\}\{R\_1+R\_2\}$$

Diodes and transistors / MOSFET

MOSFET drain current in saturation (square law)

$$I_D=\frac{1}{2}{k}_n^{\mathrm{\prime }}\frac{W}{L}(V_{GS}-V_{TH}{)}^{2}I\_D\; =\; \backslash tfrac\{1\}\{2\}k\_n\text{'}\backslash frac\{W\}\{L\}(V\_\{GS\}\; -\; V\_\{TH\})^2$$

Diodes and transistors / Zener regulator

Zener diode shunt regulator

$$I_Z=\frac{V_{in}-V_Z}{R}-\frac{V_Z}{R_L}I\_Z\; =\; \backslash frac\{V\_\{in\}\; -\; V\_Z\}\{R\}\; -\; \backslash frac\{V\_Z\}\{R\_L\}$$

Diodes and transistors / diodes

Operating point of a diode in series with a resistor (Shockley equation)

$$V_s=IR+n{V}_T\ln (1+\frac{I}{I_s})V\_s\; =\; IR\; +\; nV\_T\backslash ln\backslash left(1\; +\; \backslash frac\{I\}\{I\_s\}\backslash right)$$

Operational amplifiers / basic stages

Inverting amplifier gain and output

$$A_v=-\frac{R_f}{R_{in}}A\_v\; =\; -\backslash frac\{R\_f\}\{R\_\{in\}\}$$

Non-inverting amplifier gain and output

$$A_v=1+\frac{R_f}{R_g}A\_v\; =\; 1\; +\; \backslash frac\{R\_f\}\{R\_g\}$$

Operational amplifiers / difference amplifier

Difference amplifier output (four-resistor op-amp circuit)

$$V_{out}=\frac{R_4}{R_3+R_4}(1+\frac{R_2}{R_1})V_2-\frac{R_2}{R_1}{V}_{1}V\_\{out\}\; =\; \backslash frac\{R\_4\}\{R\_3+R\_4\}\backslash left(1+\backslash frac\{R\_2\}\{R\_1\}\backslash right)V\_2\; -\; \backslash frac\{R\_2\}\{R\_1\}V\_1$$

Operational amplifiers / integrator

Op-amp integrator output for a constant input

$$V_{out}(t)=V_0-\frac{1}{RC}{\int }_0^t{V}_{in}dtV\_\{out\}(t)\; =\; V\_0\; -\; \backslash frac\{1\}\{RC\}\backslash int\_0^t\; V\_\{in\}\backslash ,dt$$

Operational amplifiers / summing amplifier

Inverting summing amplifier output

$$V_{out}=-R_f\sum _k\frac{V_k}{R_k}V\_\{out\}\; =\; -R\_f\backslash sum\_k\; \backslash frac\{V\_k\}\{R\_k\}$$

Transients / first-order circuits

First-order (RC or RL) transient response

$$v(t)=V_f+(V_0-V_f)e^{-t\mathrm{/}\tau }v(t)\; =\; V\_f\; +\; (V\_0\; -\; V\_f)e^\{-t/\backslash tau\}$$

Time for a first-order response to reach a value

$$t=\tau \ln \frac{V_f-V_0}{V_f-v}t\; =\; \backslash tau\backslash ln\backslash frac\{V\_f\; -\; V\_0\}\{V\_f\; -\; v\}$$

Transients / second-order circuits

Step response of a series RLC circuit

$$LC{\ddot{v}}_C+RC{\dot{v}}_C+v_C=V,\alpha =\frac{R}{2L},{\omega }_0=\frac{1}{\sqrt{LC}}LC\backslash ,\backslash ddot\; v\_C\; +\; RC\backslash ,\backslash dot\; v\_C\; +\; v\_C\; =\; V,\backslash quad\; \backslash alpha\; =\; \backslash frac\{R\}\{2L\},\backslash \; \backslash omega\_0\; =\; \backslash frac\{1\}\{\backslash sqrt\{LC\}\}$$

Out of scope

• Open-ended explanation, essay writing or tutoring dialogue: it is a solver, not a chatbot.
• Questions outside its certified electrical engineering capabilities, and any question whose stated numbers it cannot all use — it refuses with the reason instead.
• High-stakes engineering, medical or legal decisions without independent review.

Limitations

• It answers what its certified capabilities cover (DC and AC circuits, transients, phasors and power, operational amplifiers, diodes and transistors, digital logic, and control systems (transfer functions, stability, Bode)); anything else is refused with a reason.
• ask() reads documented question forms and common phrasings; unusual wording may be refused — use solve() for guaranteed results.
• Results are as correct as the certified relations and their stated conditions; a certified relation is a checked model, not a claim about every physical situation.

Citation

@software{electrical_engineering_ai999x_1_0_3,
  title  = {electrical-engineering-ai999x: an offline, verified electrical engineering solver},
  author = {Farabi, Ibnul Jaif}, organization = {AI999X},
  year   = {2026}, version = {1.0.3},
  url    = {https://huggingface.co/AI999X/electrical-engineering-ai999x}
}

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Created and engineered by Ibnul Jaif Farabi · AI999X · ai999x.com