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Question

A capacitor of capacitive reactance 5 Ω is connected with AC source having voltage V=3sin(ωt+π6). Then


A
Irms=32 A
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B
Irms=352 A
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C
Instantaneous current in the circuit is 35 sin(ωt+2π3)
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D
Instantaneous current in the circuit is 352 sin(ωt+2π3)
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Solution

The correct option is C Instantaneous current in the circuit is 35 sin(ωt+2π3)
Given:

XC=5 Ω; V=3sin(ωt+π6)

On comparing the given voltage with
V=V0sin(ωt+ϕ)

We have, V0=3 V

Vrms=V02=32 V

Therefore, the rms current in the circuit is

Irms=VrmsXC=352 A

We know that in a capacitor, current leads voltage by π2.

Therefore, the instantaneous current is given by

I=V0XCsin(ωt+π6+π2)

=35sin(ωt+π6+π2)=35sin(ωt+2π3)

Hence, option (B) and (C) are the correct answers.

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