Question

When a series combination of $L$ and $R$ are connected with a $10V$, $50HZ$ A.C. source, a current 1A flows in the circuit. The voltage leads the current by a phase angle of $\pi /3$ radian. Then the resistance is

• A. 5$\Omega$
• B. 10$\Omega$
• C. 15$\Omega$
• D. 20$\Omega$

Answer 1

The correct option is A 5$\Omega$

$Vrms=10V,Irms=1A$

i.e. $tan\frac{\pi }{3}=\frac{x_L}{x_R}$

$\sqrt{3}=\frac{x_L}{R}$

also $\frac{10}{z}=1$

${10}^2=R^2\times X_L^2$

${10}^2=R^2+3^2$

$100=4R^2$

$R=5\Omega$