Question

The resistance that must be connected in series with inductance of $0.2H$ in order that the phase difference between current and electromotive force may be ${45}^{\circ }$ when the frequency is $50Hz$, is :

• A. $6.28$ ohm.
• B. $62.8$ ohm.
• C. $628$ ohm.
• D. $31.4$ ohm.

Answer 1

The correct option is B $62.8$ ohm.

Given,

$L=0.2H$

$\theta ={45}^0$

$f=50Hz$

$\omega =2\pi f=2\times 3.14\times 50=314Hz$

Current lags behind the electromotive force in the inductive circuit by phase angle $\theta$

$sin\theta =\frac{R}{\sqrt{R^2+X_L^2}}$. . . . . .(1)

$sin{45}^o=\frac{R}{\sqrt{R^2+(\omega L{)}^2}}$

$0.5=\frac{R^2}{R^2+(\omega L{)}^2}$

$R^2+(\omega L{)}^2=2R^2$

$R^2=(\omega L{)}^2$

$R=\omega L=314\times 0.2$

$R=62.8\Omega$

The correct option is B.