Question

A resistor and an inductor are connected in series across a voltage, $V=283\sin \left(314t\right)$. The current is found to be $4\sin (314t-\pi /4)$. The value of resistance of resistor is -

• A. $10\Omega$
• B. $30\Omega$
• C. $50\Omega$
• D. $70\Omega$

Answer 1

The correct option is C $50\Omega$

In LR AC circuit, current lags the voltage by an angle,

$\varphi ={\tan }^{-1}\left(\frac{X_L}{R}\right)$

Here, $\varphi =\pi /4$

$\Rightarrow X_L=R$

Further,

$V_0=i_{0}Z$

$\Rightarrow 283=4\sqrt{R^2+X_L^2}$

$\Rightarrow 2R^2=5005.56$

$\Rightarrow R=50\Omega$

Hence, option $\left(C\right)$ is the correct answer.