Question

A parallel-plate capacitor with plate area 20 cm² and plate separation 1.0 mm is connected to a battery. The resistance of the circuit is 10 kΩ. Find the time constant of the circuit.

Answer 1

Given:
Area of the plates, A = 20 cm² = 20 × 10⁻⁴ m²
Separation between the plates, d = 1 mm = 1 × 10⁻³ m,
Resistance of the circuit, R = 10 kΩ
The capacitance of a parallel-plate capacitor,

$$\begin{gathered} C=\frac{{\mathit{\in }}_{\mathit{0}}\mathit{}A}{d} \\ =\frac{8.85\times {10}^{-12}\times 20\times {10}^{-4}}{1\times {10}^{-3}} \\ =\frac{8.85\times {10}^{-12}\times 2\times {10}^{-4}}{{10}^{-3}} \\ =17.7\times {10}^{-12}\mathrm{F} \end{gathered}$$

Time constant = CR
= 17.7 × 10⁻¹² × 10 × 10³
= 17.7 × 10⁻⁸ s
= 0.177 × 10⁻⁶ s
= 0.18 μs