Question

Reactance of a coil is $157\Omega$. On connecting the coil across a source of frequency $100Hz$, the current lags behind e.m.f. by ${45}^o$. The inductance of the coil is _________.

• A. $0.25H$
• B. $0.5H$
• C. $4H$
• D. $314H$

Answer 1

The correct option is A $0.25H$

Since the phase angle is ${45}^{\circ }$,

$\frac{X_L}{R}=tan\varphi =tan{45}^{\circ }=1$

$⟹X_L=R$

$⟹\omega L=R$

$⟹2\pi fL=R$

$⟹L=\frac{R}{2\pi f}$

$=\frac{157}{2\pi \times 100}H$

$=0.25H$