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Question

In an LR series circuit , sinusoidal voltage V=V0 sin ωt is applied . It is given that L=35 mH, R=11 Ω , Vrms=220 V, ω2π =50 Hz and π=22/7.Find the amplitude of current in the steady state and obtain the phase difference between the current and voltage .Also plot the variation of current for one cycle on the given graph
1023507_85d34023da7e429bba8356b72de9a7e5.png

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Solution

Inductive reactance =XL=ωL=2π×50×35×103=3.5π=11 Ω
P
ϕ=π4
RMS current i=VrmsR2+X2L=220112+112
irms=220112=202
Maximum current Imax=Irms2=20 A
Current I=Imaxsin(ωt+ϕ)=20sin(ωt+π/4)
In above waveform, Time period, T=2π

970490_1023507_ans_46297a168f284e329e2b00859fd83c26.png

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