Q160 / 200 · MHT CET - Medical 2026 (26 April Shift 1) · Physics
The equivalent capacitance between 'P' and 'Q' is [A-area of each plate, d-separation between the plates, $\epsilon_0$ -permittivity of free space]


- A$\dfrac{A\epsilon_0}{d}$
- Correct answerB$\dfrac{2A\epsilon_0}{d}$
- C$\dfrac{3A\epsilon_0}{d}$
- D$\dfrac{4A\epsilon_0}{d}$
Solution
The given arrangement is equivalent to three capacitors connected in parallel between the terminals P and Q, as the potential difference across each section is the same.
The capacitance of a parallel plate capacitor with a dielectric is given by $C = \dfrac{K \epsilon_0 A'}{d}$.
For the three sections, the area is $A' = \dfrac{A}{3}$ and the distance between the plates is $d$.
The individual capacitances are:
$C_1 = \dfrac{K_1 \epsilon_0 (A/3)}{d} = \dfrac{1 \cdot \epsilon_0 A}{3d} = \dfrac{\epsilon_0 A}{3d}$
$C_2 = \dfrac{K_2 \epsilon_0 (A/3)}{d} = \dfrac{2 \cdot \epsilon_0 A}{3d} = \dfrac{2\epsilon_0 A}{3d}$
$C_3 = \dfrac{K_3 \epsilon_0 (A/3)}{d} = \dfrac{3 \cdot \epsilon_0 A}{3d} = \dfrac{3\epsilon_0 A}{3d}$
Since the capacitors are in parallel, the equivalent capacitance $C_{eq}$ is the sum of the individual capacitances:
$C_{eq} = C_1 + C_2 + C_3$
$C_{eq} = \dfrac{\epsilon_0 A}{3d} + \dfrac{2\epsilon_0 A}{3d} + \dfrac{3\epsilon_0 A}{3d}$
$C_{eq} = \dfrac{\epsilon_0 A}{3d} (1 + 2 + 3)$
$C_{eq} = \dfrac{6\epsilon_0 A}{3d} = \dfrac{2A\epsilon_0}{d}$
Answer: $\dfrac{2A\epsilon_0}{d}$
The capacitance of a parallel plate capacitor with a dielectric is given by $C = \dfrac{K \epsilon_0 A'}{d}$.
For the three sections, the area is $A' = \dfrac{A}{3}$ and the distance between the plates is $d$.
The individual capacitances are:
$C_1 = \dfrac{K_1 \epsilon_0 (A/3)}{d} = \dfrac{1 \cdot \epsilon_0 A}{3d} = \dfrac{\epsilon_0 A}{3d}$
$C_2 = \dfrac{K_2 \epsilon_0 (A/3)}{d} = \dfrac{2 \cdot \epsilon_0 A}{3d} = \dfrac{2\epsilon_0 A}{3d}$
$C_3 = \dfrac{K_3 \epsilon_0 (A/3)}{d} = \dfrac{3 \cdot \epsilon_0 A}{3d} = \dfrac{3\epsilon_0 A}{3d}$
Since the capacitors are in parallel, the equivalent capacitance $C_{eq}$ is the sum of the individual capacitances:
$C_{eq} = C_1 + C_2 + C_3$
$C_{eq} = \dfrac{\epsilon_0 A}{3d} + \dfrac{2\epsilon_0 A}{3d} + \dfrac{3\epsilon_0 A}{3d}$
$C_{eq} = \dfrac{\epsilon_0 A}{3d} (1 + 2 + 3)$
$C_{eq} = \dfrac{6\epsilon_0 A}{3d} = \dfrac{2A\epsilon_0}{d}$
Answer: $\dfrac{2A\epsilon_0}{d}$
Hence, the correct answer is option: 'B'.