Capacitor charging calculator

Worked example

Find V, the p.d. at time t. Given: supply p.d. V0 = 9.00 V; time t = 5.00 s; time constant RC τ = 5.00 s.

1. Write the equation
   V = V₀ (1 − e^{−t / τ})
2. Substitute the values
   V = 9 × (1 − e^{−5 ÷ 5})
3. Calculate
   V = 5.68909 V
4. Give the answer to 3 significant figures
   V = 5.69 V

Symbols and units

Capacitor charging: rearranged

• To find p.d. at time t: V = V₀ (1 − e^{−t / τ})
• To find supply p.d.: V₀ = V / (1 − e^{−t / τ})
• To find time: t = −τ ln(1 − V / V₀)
• To find time constant RC: τ = −t / ln(1 − V / V₀)

Exam tip

The p.d. approaches V₀ but never reaches it. After one time constant it is about 63% of V₀.

Common questions

What is the formula for capacitor charging?

The equation is V = V0 (1 − e−t / τ), where V is the p.d. at time t (V); V0 is the supply p.d. (V); t is the time (s); τ is the time constant RC (s).

What units should I use for capacitor charging?

In SI units: p.d. at time t in V, supply 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 (1 − e−t / τ)?

Rearranging gives these forms: to find p.d. at time t: V = V0 (1 − e−t / τ). to find supply p.d.: V0 = V / (1 − e−t / τ). to find time: t = −τ ln(1 − V / V0). to find time constant RC: τ = −t / ln(1 − V / V0).