In the circuit shown in the figure, the battery B supplies 12 V. We have to find (a) the charge on each capacitor when switch is closed and (b) when (later) switch is also closed. We make take , , , and .

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Data of the problem are

,

,

,

,

and the EMF of the battery B is

(a)

Let the switch be closed first. Let the magnitude of charge on capacitors and be . As these capacitors are connected in series, potential difference across them will add to 12 V. That is

and

And let the charge across capacitors and be . Then

(b)

When the switch is also closed, the circuit has effectively two capacitors in series one is parallel combination of and with resultant capacitance , the other is parallel combination of and with resultant capacitance . Therefore, the effective capacitance in the circuit will be

The combined charge on the capacitors and , or the equal combined charge on the capacitors and will be

Let the charge on be We have

Similarly, let the charge on be . We have