Question

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \,V , 50 \,Hz$ supply, a current of $0.5$ A flows in the circuit. The current differs in the phase from applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is

• A. $10 \Omega$
• B. $3 \Omega$
• C. $12 \Omega$
• D. $15 \Omega$

Answer 1

Answer: (C)

Given situation following the figure below,

$12 \,V , 50 \,Hz$
Given for AC circuit,
$V_{ rms }=12 \,V$
frequency , $f=50 Hz$,
current, $I=0.5 A$
phase difference, $\phi=\frac{\pi}{3}$
$\therefore $ Impedance of the AC circuit,
$Z=\frac{V_{ rms }}{I}=\frac{12}{0.5} \Rightarrow Z=24 \Omega$
Power factor,
$\Rightarrow \cos \phi=\frac{R}{Z} \Rightarrow \cos \frac{\pi}{3}=\frac{R}{24} \Rightarrow \frac{1}{2}=\frac{R}{24} \Rightarrow R=12 \Omega$