The figure shows a capacitor C with an initial charge Q0 connected in series with a resistor. When the switch is closed the capacitors starts discharging. If i be the instantaneous current and q be the instantaneous charge on the capacitor then, using Kirchoff's voltage law or On integrating, we have ln|q| =
At t = 0, q = Qo Þ K = ln|Qo|
And, the instantaneous current through the capacitor is
The current magnitude at t = 0 is and the direction of I is opposite is that shown
The discharging of a capacitor may be summarised as
q = Qoe-t/t
i = Ioe-t/t.
v = Voe-t/t.
where t = RC is the time constant, Q0 I0 and V0 are the initial charge, current and potential difference across the capacitor.
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