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CUET · PHYSICS · PYQ PAPER 2023

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

  1. A \( \left( \frac{2k + 3}{k} \right) V_0 \)
  2. B \( \left( \frac{2k + 3}{5k} \right) V_0 \)
  3. C \( \left( \frac{5k}{2k + 3} \right) V_0 \)
  4. D \( \left( \frac{k + 3}{5k} \right) V_0 \)
Verified Solution

Answer & Solution

Correct Answer

(B) \( \left( \frac{2k + 3}{5k} \right) V_0 \)

Step-by-step Solution

Detailed explanation

\( Q = C_0 V_0 = \frac{\epsilon_0 A V_0}{d} \) \( C = \frac{\epsilon_0 A}{d - t + \frac{t}{k}} = \frac{\epsilon_0 A}{d - \frac{3}{5}d + \frac{\frac{3}{5}d}{k}} \)…