First slide

Displacement current

Question

A parallel plate condenser has conducting plates of radius 12 cm separated by a distance of 5 mm. It is charged with a constant charging current of 0.16 A, the rate at which the potential difference between the plates change is

Moderate

Solution

$\begin{array}{rcl} i_{d} & = & \frac{ε_{0} A}{d} (\frac{dV}{dt}); \\ \frac{dV}{dt} & = & \frac{i_{d} . d}{ε_{0} A} \\ = & \frac{4 π . i_{d} . d}{4 π \in_{0} . {πr}^{2}} \\ = & 9 x 10^{9} . \frac{16 x 10^{- 2} x 5 x 10^{- 3} x 4 π}{π . 12 x 12 x 10^{- 4}} \\ \frac{dV}{dt} & = & 2 x 10^{9} {Vs}^{- 1} \end{array}$

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