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PhysicsClass 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?
Question: 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?

Answer

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 \(=6.9\;\mu \text{A}.\)
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