1
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Question

# An a.c generator supplying voltage E=10sinωt V to a circuit which consists of a resistor of resistance 3 Ω and an inductor of reactance 4 Ω as shown in the figure. The voltage across the inductor at t=πω is

A
2 V
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B
10 V
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C
Zero
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D
4.8 V
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Solution

## The correct option is D 4.8 VImpedance of the circuit Z=√R2+X2L =√32+42=5 Ω Power factor of the circuit cosϕ=RZ=35 ⇒ϕ=53∘ Therefore, current in the circuit is ∵i=E0Zsin(ωt−53∘)=2sin(ωt−53∘) Voltage across the inductor VL=Ldidt=2ωLcos(ωt−53∘) At t=πω, VL=8cos(π−53∘) (∵ωL=4) VL=−8cos53∘=−8×35 ∴VL=−4.8 V i.e. potential across inductor lags behind.

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