Alternating Current

JEE Main level, single correct, medium

13 of 190

Question 13 of 190

A parallel plate capacitor has a capacitance C=200pFC=200pF. It is connected to 230V230V ac supply with an angular frequency 300rads−1300rad{s}^{-1}. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

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Answer: (D) 13.8μA13.8\mu A and 13.8μA13.8\mu A

By Maxwell's equation for a time varying voltage (AC voltage), both conduction and displacement currents are the same. Therefore,
Idisplacement=Iconduction=VrmsXC=Vrms1ωC=230×300×200×10−12=13.8μA{I}_{displacement}={I}_{conduction} =\dfrac{{V}_{rms}}{{X}_{C}} =\dfrac{{V}_{rms}}{\dfrac{1}{\omega C}} =230\times 300\times 200\times {10}^{-12} =13.8\mu A

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