Question

Parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference of 18 V. The battery is then disconnected, and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be:

A) 6 V
B) 9 V
C) 12 V
D) 18 V

Answer 1

The final potential difference across the combination of capacitors will be 18 V. therefore, the correct option is D) 18 V.

Step-by-step explanation:

Since the capacitors are in parallel, the charge remains conserved and the potential difference across each capacitor will be the same. Using the formula V = Q/C, and knowing the charge in the system does not change, the increased capacitance reduces the potential difference across the original C capacitor, which then has the same reduced potential difference across the 3C capacitor, as they share the same charge.

In this problem, we have two parallel plate capacitors with capacities C and 3C connected in parallel combination and charged to a potential difference of 18 V. The battery is then disconnected, and the space between the plates of the capacitor with capacity C is completely filled with a material of dielectric constant 9.

When the dielectric is added, the capacity of the capacitor with capacity C is multiplied by the dielectric constant, so it becomes 9C. The potential difference across capacitors in parallel remains the same, so the final potential difference across the combination of capacitors will be 18 V.

Therefore, the correct answer is D) 18 V.