Capacitor discharge calculator

Worked example

Find V, the p.d. at time t. Given: starting p.d. V0 = 12.0 V; time t = 20.0 s; time constant RC τ = 10.0 s.

1. Write the equation
   V = V₀ e^{−t / τ}
2. Substitute the values
   V = 12 × e^{−20 ÷ 10}
3. Calculate
   V = 1.62402 V
4. Give the answer to 3 significant figures
   V = 1.62 V

Symbols and units

Capacitor discharge: rearranged

• To find p.d. at time t: V = V₀ e^{−t / τ}
• To find starting p.d.: V₀ = V e^{t / τ}
• To find time: t = −τ ln(V / V₀)
• To find time constant RC: τ = −t / ln(V / V₀)

Exam tip

Use the same unit for t and τ. V must be smaller than V₀ when you solve for time.

Common questions

What is the formula for capacitor discharge?

The equation is V = V0 e−t / τ, where V is the p.d. at time t (V); V0 is the starting p.d. (V); t is the time (s); τ is the time constant RC (s).

What units should I use for capacitor discharge?

In SI units: p.d. at time t in V, starting p.d. in V, time in s, time constant RC in s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange V = V0 e−t / τ?

Rearranging gives these forms: to find p.d. at time t: V = V0 e−t / τ. to find starting p.d.: V0 = V et / τ. to find time: t = −τ ln(V / V0). to find time constant RC: τ = −t / ln(V / V0).