# Differential equation for Voltage across a capacitor.

Discussion in 'General Electronics Chat' started by Electromech man, Dec 9, 2010.

1. ### Electromech man Thread Starter New Member

May 2, 2009
8
0
Good day folks,

I know the differential equation for time varying voltage across an inductor is v(t)=L*di(t)/dt.

Can anyone tell me the equation for time varying voltage across a capacitor?

Regards.

2. ### tyblu Active Member

Nov 29, 2010
199
16
taken from http://en.wikipedia.org/wiki/Capacitor#Current-voltage_relation

$i_C(t) = C\frac{dv(t)}{dt} \\
\int_{t_0}^{\tau} i_C(t)dt = C\int_{t_0}^{\tau} \frac{dv(t)}{dt}dt \\
\int_{t_0}^{\tau} i_C(t)dt = C [ v(\tau) - v(t_0) ] \\
v(\tau) = \frac{1}{C}\int_{t_0}^{\tau} i_C(t)dt + v(t_0)
$

Last edited: Dec 9, 2010