Question

In an LR series circuit , sinusoidal voltage V=$V_0$ sin $\omega$t is applied . It is given that L=35 mH, R=11 $\Omega$ , V${}_{rms}$=220 V, $\frac{\omega }{2\pi }$ =50 Hz and $\pi$=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

Answer 1

Inductive reactance $=X_L=\omega L=2\pi \times 50\times 35\times {10}^{-3}=3.5\pi =11$ $\Omega$

P

$\Rightarrow \varphi =\frac{\pi }{4}$

RMS current $i=\frac{V_{rms}}{\sqrt{R^2+X_L^2}}=\frac{220}{\sqrt{{11}^2+{11}^2}}$

$i_{rms}=\frac{220}{11\sqrt{2}}=\frac{20}{\sqrt{2}}$

Maximum current $I_{max}=I_{rms}\sqrt{2}=20$ $A$

Current $I=I_{max}\sin (\omega t+\varphi )=20\sin (\omega t+\pi /4)$

In above waveform, Time period, $T=2\pi$