Capacitor Charging & Time Constants

When a capacitor charges through a resistor, it doesn't fill up at a steady rate — it charges fast at first, then slower and slower as it gets closer to full voltage. The time constant tells you how quickly this slowdown happens: after one time constant, the capacitor has reached about 63 percent of its final voltage.

τ = R · C

• τ — time constant (s): the time to reach about 63 percent of full charge
• R — resistance (Ω): how much the resistor limits the charging current
• C — capacitance (F): how much charge the capacitor can store per volt

A 1000 Ω resistor charges a 0.001 F capacitor. What is the time constant?

• R = 1000 Ω
• C = 0.001 F

1. τ = R · C
2. τ = 1000 Ω · 0.001 F

τ = 1 s

If the resistor is changed to 2000 Ω with the same 0.001 F capacitor, what is the new time constant?

• 2 s
• 1 s
• 4 s

After exactly one time constant has passed, roughly what percent of full voltage has the capacitor reached?

• 37%
• 50%
• 63%