Question

A parallel plate capacitor has plate area 100 m² and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF. The value of ε₀ = 8.85 × 10⁻¹² F m⁻¹. The value of 'x' to the nearest integer is __________.

Hint:

Capacitance with a partial slab of thickness $t$ is $C = \frac{\epsilon_0 A}{d - t + t/K}$.

Answer 1

Correct Answer: 161

Step 1: This is a series combination of two capacitors: one with air ($d=5$) and one with dielectric ($d=5$).
Step 2: $C_{air} = \frac{\epsilon_0 A}{d/2} = \frac{8.85 \times 10^{-12} \times 100}{5} = 177 \text{ pF}$.
Step 3: $C_{dielectric} = \frac{K \epsilon_0 A}{d/2} = 10 \times 177 = 1770 \text{ pF}$.
Step 4: $C_{eq} = \frac{C_1 C_2}{C_1 + C_2} = \frac{177 \times 1770}{177 + 1770} = \frac{177 \times 1770}{1947} \approx 160.9 \approx 161 \text{ pF}$.