All courses › Electric Circuits › RC Time Constant

RC Time Constant

When a capacitor charges or discharges through a resistor, the voltage follows an exponential curve toward its final value. How fast this happens is set by the time constant τ = RC. After one time constant the voltage has reached 63% of the way to the final value, and after five time constants it is considered practically finished.

\tau=RC

time constant for an RC circuit

u(t)=U(1-e^{-t/\tau})

charging toward U

u(t)=U_0e^{-t/\tau}

discharging from U_0

Symbols

$\tau$	time constant	s
$R$	resistance	$\Omega$
$C$	capacitance	F
$U$	final value (charging)	V

Example

$R=2$ kΩ, $C=100$ µF, charging toward $10$ V:

$\tau=RC=0.2$ s. After $\tau$ : $u\approx0.632\cdot10\approx6.3$ V.

Set

t=0

and let

t\to\infty

in your formula and check that you get the start and final values.

Practise capacitors and inductors for free →

← Inductor · Sine Waves and RMS →

Part of Electric Circuits: Capacitors and inductors.