First slide

Maxwell's displacement current

Question

A parallel plate capacitor made of circular plates each of radius $10.0 c m$ has a capacitance $200 p F$ . The capacitor is connected to a $200 V a c$ supply with an angular frequency of $100 r a d / s$ . The rms value of the conduction current is ______ $μ A$

Moderate

Solution

Given : $E r m s = 200 V, ω = 100 r a d / s$
Capacitance, $C = 200 \times 10^{- 12} F$
RMS value of the conduction current is $I r m s = \frac{E r m s}{X_{C}}$
$\Rightarrow I r m s = \frac{E r m s}{1 / ω C} = ω C \times E r m s$
$\Rightarrow I r m s = 100 \times 200 \times 10^{- 12} \times 200 = 4 \times 10^{- 6} A = 4 μ A$

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