Electric circuit simulator
Pick a circuit and a source, set R, L and C: the time response, oscilloscope, Bode plot and calculations update live. For high school and university physics.
Circuit and source
Circuit diagram
Transient response
Calculations
Sinusoidal steady state: Bode plot
Build a circuit
The “Build a circuit” tab lets you put together any circuit: batteries, a signal generator (sine, square, triangle), lamps, resistors, capacitors, inductors, diodes, LEDs, switches, changeover switches, ammeters and voltmeters (DC or AC), ground. Place components from the palette and connect them by dragging wires from their terminals: current flows at once (animated dots, conventional current or electron flow), lamps glow according to the power they receive and meters show their reading. With a capacitor, an inductor or a generator, the circuit evolves in time, in slow motion if needed: place probes Y1 and Y2 to see voltages on the oscilloscope (trigger, XY mode), and draw the Bode plot of a filter. Click a wire to check the junction rule. Over twenty examples are ready: series and parallel, Ohm's law, short circuit, capacitor charging and discharging, delayed lighting with an inductor, RLC oscillations, rectifier, LED with a protective resistor, filters and resonance… The circuit exports to SVG or LaTeX (circuitikz) and can be shared with a link.
How to use the RC, RL, RLC simulator
- Pick the circuit (series RC, RL, RLC, LC, parallel RLC) or a ready-made one: capacitor charging and discharging, current build-up, underdamped, critical and overdamped responses, filters, resonance, tank circuit…
- Set the components with the fields (choice of units) or the logarithmic sliders, plus the source's internal resistance and the coil's resistance.
- Pick the source: step, square, sine or triangle, with the initial conditions.
- Read the results: curves, oscilloscope (two channels, XY mode), energies, phase portrait, Bode plot, calculations with numbers. Cursors measure times and voltages.
How it is computed
The transient response comes from integrating the circuit's differential equations with the 4th-order Runge-Kutta method, with a step much smaller than the time constant, so curves are valid for any source. The Bode plot uses the complex impedances $\underline{Z}_R = R$, $\underline{Z}_L = r + \mathrm{j}L\omega$ and $\underline{Z}_C = 1/(\mathrm{j}C\omega)$; the gain is $G_{\mathrm{dB}} = 20\log|\underline{H}|$.
Frequently asked questions
How do I find the time constant on the curve?
The tangent at the origin meets the asymptote at $t = \tau$, when the voltage has covered 63% of its change. Tick “Tangent at the origin and τ”, or place the cursors.
Why is the voltage resonance not exactly at $f_0$?
Across the capacitor, the peak is at $f_r = f_0\sqrt{1 - 1/(2Q^2)}$, which only exists if $Q > 1/\sqrt{2}$. The current resonance (voltage across R) is always at $f_0$.
Can I build my own circuit with lamps and batteries?
Yes: in the “Build a circuit” tab, place batteries, lamps, resistors, switches, ammeters and voltmeters, then connect them with wires. The simulator computes every voltage and current at once: lamps glow more or less brightly, meters show their readings, and a message flags a short circuit, an open circuit or a lamp burning out.
How does the simulator compute the circuit I build?
With nodal analysis, like professional software: Kirchhoff's laws (junction and loop rules) and each component's law give a system of equations. Wires and ammeters have an almost zero resistance, voltmeters 10 MΩ, each lamp a constant resistance. With capacitors and inductors, the time response is computed step by step with the trapezoidal method; diodes and LEDs follow the Shockley law, solved with Newton's method; the Bode plot uses the complex impedances jCω and jLω.
Can I watch a capacitor charge on the oscilloscope?
Yes: place a battery, a resistor, a capacitor and a changeover switch (or open the “Charging and discharging a capacitor” example), then put probe Y1 across the capacitor and add ground. The oscilloscope plots u_C(t) while charging, then discharging when you flip the switch; the simulation speed adapts to the time constant τ = RC, and the 63% reading gives τ.
Are my settings sent anywhere?
No: everything runs in your browser. The share link contains the circuit itself.
Guided activities
1. Charging a capacitor (RC)
With R = 1 kΩ and C = 1 µF, the time constant is τ = RC = 1 ms. Under a 5 V step, the capacitor voltage reaches 63% of 5 V (3.16 V) after τ, and 99% after 5τ = 5 ms: the usual length of the transient. Find τ three ways: tangent at the origin, reading 63% with the cursors, and the displayed calculation. Double R: τ doubles.
2. The three regimes of a series RLC
With L = 10 mH and C = 1 µF, the natural frequency is f₀ = 1/(2π√(LC)) ≈ 1,592 Hz, and the critical resistance R = 2√(L/C) = 200 Ω.
- R = 20 Ω: underdamped, the voltage oscillates as it decays; measure the pseudo-period with the cursors and compare it with 1/f₀.
- R = 200 Ω: critically damped, the fastest return to equilibrium with no overshoot.
- R = 1 kΩ: overdamped, a slow return without oscillation.
The phase portrait and energy curves show energy swapping between the capacitor (electric) and the coil (magnetic), and dissipating in the resistor.
3. RC low-pass filter
With R = 1 kΩ and C = 1 µF, the cut-off frequency is f_c = 1/(2πRC) ≈ 159 Hz. On the Bode plot the gain is −3 dB there, then falls by 20 dB per decade; the phase goes from 0 to −90°, with −45° at f_c. Feed a square wave at 50 Hz then 2 kHz to the oscilloscope: at high frequency the filter “integrates” the signal into a triangle.
4. Resonance and quality factor
For a series RLC, the quality factor is Q = (1/R)√(L/C). With the values above and R = 20 Ω, Q = 5: current resonance is sharp and the bandwidth is f₀/Q ≈ 318 Hz. Increase R: the curve flattens. Compare with the capacitor voltage, whose peak shifts below f₀.
Common lab mistakes
- Forgetting internal resistances of the generator (often 50 Ω) and the coil: they change the damping. The simulator lets you set both.
- Measuring τ on too wide a timebase: zoom so the transient fills the screen, as on a real oscilloscope.
- Mixing up f and ω: ω = 2πf; an error by a factor of 6.28 usually gives it away.
Exporting for a lab report
Curves export as SVG or PNG, data as CSV (time domain and Bode) for a spreadsheet or Python, and calculations as LaTeX. The share link keeps the circuit: handy for setting students an exercise.
Guide written and checked by the Otoolia team · updated 3 November 2026.