Question

In a given R - L circuit, I = 10 A and power loss in circuit is 1 kW, then

• A. Inductance of the circuit is $\frac{\sqrt{3}}{10\pi }H$
• B. Resistance of the circuit is $10\sqrt{3}\Omega$
• C. Power factor is 0.5
• D. Voltage is ${60}^o$ ahead of current

Answer 1

Answer: (A), (C), (D)

The correct options are
A Inductance of the circuit is $\frac{\sqrt{3}}{10\pi }H$
C Power factor is 0.5
D Voltage is ${60}^o$ ahead of current

$P=i^{2}R\Rightarrow 1000={10}^2\times R\Rightarrow R=10\Omega$
$V=IZ\Rightarrow 200=10\sqrt{R^2+X_L^2}\Rightarrow X_L=10\sqrt{3}$
$X_L=\omega L\Rightarrow L=\frac{X_L}{2\pi 50}=\frac{\sqrt{3}}{10\pi }$
$\varphi ={60}^o\therefore \text{Power factor}=\cos \varphi =\frac{1}{2}$