First slide

Capacitance

Question

Two parallel plate capacitors of capacitance C and 2C are connected in parallel and charged to a potential difference V by a battery. The battery is then C disconnected and the space between the plates of capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes:

Moderate

A

$\frac{V}{K + 1}$
B

$\frac{2 V}{K + 1}$
C

$\frac{3 V}{K + 2}$
D

$\frac{3 V}{K + 3}$

Solution

Total original capacitance of system = C + 2C = 3C
if C is filled with delectric of K. dielectric constant K.
Then C' = KC
Now, capacitance of system C" = C' +2C = (K + 2) C
$∴ Pot. difference = \frac{Q}{C^{''}} = \frac{3 CV}{(K + 2) C} = \frac{3 V}{K + 2}$ .

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