First slide

Capacitance

Question

A 2μF capacitor is charged to a potential difference 30V and the charging battery is disconnected. It is then connected to a series combination of capacitors $C_{1}$ = 2μF and $C_{2}$ = 4μF, as shown. Both $C_{1} and C_{2}$ are initially uncharged. When the switch S is closed, charge redistributes. Final potential difference across $C_{1}$ will be :

Moderate

A

8 V
B

10 V
C

12 V
D

18 V

Solution

Initial charge = 60μC
From diagram $\frac{60 - q}{2} = \frac{q}{2} + \frac{q}{4}$
$\Rightarrow q = 24 μC$
Voltage on $C_{1} = \frac{q}{2} = 12 V$

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