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11.11.1 Charging of CapacitorThe figure shows a circuit arrangement in which a capacitor in series with a resistor is connected across a battery of emf E through a switch S.
When the switch S is closed the current starts flowing and the capacitor starts charging. If I be the instantaneous charge on the capacitor, then applying Kirchoff’s Voltage Law.
Since I = , the above equations may be rearranged as
RC = CE - q
After integrating we get
ln |CE - q| =
At t = 0, q, = 0 Þ K = ln |CE|
\ q = CE ( 1 - e-t/RC)
The instantaneous potential difference across the capacitor is
The instantaneous current through the circuit is
The graphs showing the variation of q, v and i with time are shown as below.
The charging of a capacitor may be summarised as
q = Qmax (1 - e-t/t)
v = Vmax (1 - e-t/t)
i = Imax e-t/t
Where Qmax = CE; Vmax = E; Imax =E/R and t = RC (time constant)
The time constant t is defined as the time during which charge on the capacitor rises to 0.63 times the maximum value.
when t = t, q = qmax (1-e-1)
or q = 0.63 qmax
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