With τ = RC = 2 s, what fraction of V₀ has the capacitor reached at t = 2 s?

You can work it out this way: use V(t) = V₀(1 − e^(−t/τ)) and evaluate at t = τ.

If you increase the plate separation d, how does capacitance change?

You can work it out this way: use C = ε₀A/d and think about the direction of the change.

Two identical capacitors are connected in parallel, then separately in series. What is the total capacitance in each case?

Parallel: C_total = C₁ + C₂; Series: 1/C_total = 1/C₁ + 1/C₂.

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Pro 🔒~30 min

Capacitors & RC Circuits

Watch exponential charging and discharging governed by the RC time constant

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How it works

A capacitor stores charge on two parallel plates separated by a dielectric. Its capacitance C = ε₀A/d depends on plate area A and separation d. In an RC circuit, charging follows V(t) = V₀(1 − e^(−t/RC)) and discharging follows V(t) = V₀e^(−t/RC). The time constant τ = RC is the time to reach approximately 63% of the final voltage during charging, and the energy stored at full charge is U = ½CV².

Step-by-step

Set capacitance, resistance, and battery voltage with the free-tier sliders, then click Charge to watch the exponential curve build up.
Click Discharge to release the stored energy.
Unlock Pro mode to adjust plate geometry and see how it directly maps to capacitance.

Key formulas

$C = \frac{Q}{V} = \frac{\varepsilon_0 A}{d}$ Capacitance from geometry
$V(t) = V_0\left(1 - e^{-t/RC}\right)$ Charging voltage over time
$V(t) = V_0\,e^{-t/RC}$ Discharging voltage over time
$\tau = RC$ RC time constant
$U = \frac{1}{2}CV^2$ Energy stored in capacitor

Frequently asked questions

With τ = RC = 2 s, what fraction of V₀ has the capacitor reached at t = 2 s?: You can work it out this way: use V(t) = V₀(1 − e^(−t/τ)) and evaluate at t = τ.
If you increase the plate separation d, how does capacitance change?: You can work it out this way: use C = ε₀A/d and think about the direction of the change.
Two identical capacitors are connected in parallel, then separately in series. What is the total capacitance in each case?: Parallel: C_total = C₁ + C₂; Series: 1/C_total = 1/C₁ + 1/C₂.