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## QuestionPhysicsClass 12

A parallel plate capacitor (figure) made of circular plates each of radius $$R=6.0$$  cm has a capacitance $$C=100$$  pF. The capacitor is connected to a $$230\;\text{V}$$  ac supply with a (angular) frequency of $$300\;\text{rad s}^{-1}.$$
What is the rms value of the conduction current?

Radius of each circular plate, $$R=6.0\;\mathrm{cm}=0.06 \;\text{m}$$
Capacitance of a parallel plate capacitor, $$C=100\;\mathrm{pF}=100\times 10^{-12}\;\text{F}$$
Supply voltage, $$V=230\;\text{V}$$
Angular frequency, $$\omega =300\;\mathrm{rad\;s}^{-1}10^{-11}$$
Rms value of conduction current, $$I=\frac V{X_C}$$
Where,
Capacitive reactance
$$X_C=\frac 1{\mathit{\omega C}}$$
$$\therefore \quad I=V\times \mathit{\omega C}$$
$$=230\times 300\times 100\times 10^{-12}$$
$$=6.9\times 10^{-6}\;\text{A}$$
$$=6.9\;\mu \text{A}$$
Hence, the rms value of conduction current is $$=6.9\;\mu \text{A}.$$