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

Install · Capability guide · 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 1.0.0

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.

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.
• 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 1.0.0 (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

Quickstart

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-1.0.0-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.

Command line: electrical-engineering-ai999x "<question>", electrical-engineering-ai999x --capabilities. The outputs above were produced by running this exact code on electrical-engineering-ai999x 1.0.0.

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.

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_0,
  title  = {electrical-engineering-ai999x: an offline, verified electrical engineering solver},
  author = {Farabi, Ibnul Jaif}, organization = {AI999X},
  year   = {2026}, version = {1.0.0},
  url    = {https://huggingface.co/AI999X/electrical-engineering-ai999x}
}

Contact

Questions, bug reports and requests: open a discussion on https://huggingface.co/AI999X/electrical-engineering-ai999x/discussions or visit https://ai999x.com.

Support the project

electrical-engineering-ai999x is free and open source. If it helps you, you can support further development on Buy Me a Coffee.

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