How to Use the RC Circuit Calculator
An RC circuit combines a resistor (R) and a capacitor (C) in series. When a DC voltage source is connected, the capacitor does not charge instantly — it charges (or discharges) exponentially over time, governed by the circuit's time constant, τ = R × C, measured in seconds when R is in ohms and C is in farads. This calculator finds τ, the capacitor's voltage and the circuit's current at any moment during charging or discharging, and how far through the process the circuit has progressed.
How the calculation works
Enter the resistance and capacitance (each with its own unit selector), the supply voltage (or the capacitor's initial voltage if discharging), the elapsed time since the switch closed, and whether the capacitor is charging or discharging. The calculator converts R and C to base SI units (ohms and farads) and multiplies them to get the time constant τ = RC. For a charging capacitor, voltage rises according to Vc(t) = V(1 − e^(−t/τ)) and current falls according to I(t) = (V/R)e^(−t/τ), starting at V/R and decaying toward zero. For a discharging capacitor, voltage falls according to Vc(t) = V₀e^(−t/τ), and the discharge current follows the same exponential decay from V₀/R. The "Percent Complete" result reports how far the exponential curve has progressed: 1 − e^(−t/τ), expressed as a percentage.
Common mistakes
- Mixing units: resistance and capacitance must be converted to ohms and farads before multiplying — 1 kΩ × 1 µF is not 1, it's 10³ × 10⁻⁶ = 10⁻³ s = 1 ms. Use the unit selectors so the conversion happens automatically.
- Assuming linear charging: a capacitor does not charge at a constant rate. It charges fastest at t = 0 and slows as it approaches the supply voltage — after 1τ it is only about 63.2% charged, not 100%.
- Ignoring how much the timescale can vary: a 1 MΩ resistor with a 1 µF capacitor gives a 1-second time constant, while a 1 Ω resistor with the same capacitor gives a 1-microsecond time constant — component values change circuit speed by orders of magnitude.
Real-world applications
- RC circuits set timing in oscillators, debounce circuits, and camera-flash charge circuits.
- RC low-pass and high-pass filters use the same R and C values to set a cutoff frequency, f_c = 1/(2πRC), that separates signal frequencies.
- Snubber circuits and power-supply smoothing capacitors rely on predictable charge/discharge timing to protect switches and reduce ripple.
- Understanding τ helps size components so a circuit settles fast enough (small τ) or holds a voltage long enough (large τ) for the application.