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

Question

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

Infinity Learn · Accepted Answer

The capacitors are connected in parallel. So, the resultant capacitance $$=C+2C=3C$$∴Total charge Q $$=$$ $$3$$ CVWhen the capacitor of capacity C is filled with dielectric, its capacitance becomes KC. The new resultant capacitance becomes C′$$=KC+2C=(K+2)C$$.As charge remains the same, Q $$=$$ $$3CV$$∴ QC′$$=3CV(K+2)C=3VK+2$$

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