Question

When an inductor $L$ and a resistor $R$ in series are connected across a $12V,50Hz$ 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,

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