Question

In an LR series circuit, a sinusoidal voltage of $V=$ $V_0\sin \omega t$ is applied. It is given that $L=35mH,R=11\Omega ,$$V_{rms}=220V$, $\frac{\omega }{2\pi }=50Hz$ and $\pi =22/7$. Which of the following is (are) correct.

• A. Amplitude of current in the steady state is 10 $A$.
• B. Amplitude of current in the steady state is 20 $A$.
• C. Phase difference between the current and voltage is π/4
• D. Phase difference between the current and voltage is π/2

Answer 1

Answer: (B), (C)

Phase difference between the current and voltage is π/4

We know that
$X_L=\omega L$
so, $X_L=$ $11\Omega$
Impedance of the circuit will be
$Z=\sqrt{X_L^2+R^2}=11\sqrt{2}\Omega$
and
$i_0=\frac{220\sqrt{2}}{Z}$

$⟹$$i_0=20A$

$\tan \varphi =\frac{11}{11}=1\Rightarrow \varphi =\pi /4$
So, Equation of current will be
$i=20\sin (\omega t-\pi /4)$