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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.
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Solution
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,
\[C = \frac{\in_0 A}{d}\]
\[ = \frac{8 . 85 \times {10}^{- 12} \times 20 \times {10}^{- 4}}{1 \times {10}^{- 3}}\]
\[ = \frac{8 . 85 \times {10}^{- 12} \times 2 \times {10}^{- 4}}{{10}^{- 3}}\]
\[ = 17 . 7 \times {10}^{- 12} F\]
Time constant = CR
= 17.7 × 10−12 × 10 × 103
= 17.7 × 10−8 s
= 0.177 × 10−6 s
= 0.18 μs
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