A parallel plate capacitor A is filled with a dielectric whose dielectric constant varies with applied voltage as K=V. Initially A is uncharged. An identical capacitor B of capacitance $C_{0}$ with air as dielectric is connected to voltage source $V_{0} = 30 V$ and then connected to the first capacitor after disconnecting the voltage source. The charge and voltage on capacitor

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B are 5C₀ and 5V

B are 5C₀ and 25V

A are 25C₀ and 25V

A are 25C₀ and 5V

answer is B, C.

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Detailed Solution

Common $p . d, V_{C} = \frac{0 + (30) C_{0}}{{KC}_{0} + C_{0}} \Rightarrow V_{C} = \frac{30}{K + 1} = \frac{30}{V_{C} + 1}$
$\Rightarrow V_{C}^{2} + V_{C} = 30 \Rightarrow V_{C} = 5 V Q_{A} = C_{A} V_{C} = {KC}_{0} V_{C}, Q_{B} = C_{B} V_{C} = C_{0} (5)$