Question

A parallel plate capacitor filled with air has an area of 6 cm² and plate separation of 3 mm. Calculate its capacitance.

Hint:

Capacitance increases with area and decreases with separation; use SI units for consistency.

Answer 1

Capacitance of a parallel plate capacitor:
\[ C = \epsilon_0 \frac{A}{d}, \] where \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), \( A = 6 \, \text{cm}^2 = 6 \times 10^{-4} \, \text{m}^2 \), \( d = 3 \, \text{mm} = 0.003 \, \text{m} \).
\[ C = 8.85 \times 10^{-12} \times \frac{6 \times 10^{-4}}{0.003} = 8.85 \times 10^{-12} \times 0.2 = 1.77 \times 10^{-12} \, \text{F} = 1.77 \, \text{pF}. \] Answer: 1.77 pF.