Question

A coil has an inductance of 0.7 henry and is joined in series with a resistance of $220\Omega$ . When the alternating emf of 220 V at 50 Hz is applied to it then the phase through which current lags behind the applied emf and the wattless component of current in the circuit will be respectively

• A. ${30}^o,1A$
• B. ${45}^o,0.5A$
• C. ${60}^o,1.5A$
• D. None of these

Answer 1

The correct option is B ${45}^o,0.5A$

$L=0.7H,R=220\Omega ,{\epsilon }_0=220V,v=50Hz$

This is an L - R circuit
Phase difference,

$\tan \varphi =\frac{X_L}{R}=\frac{\omega L}{R}=\frac{2\pi vL}{R}$

$[X_L=2\pi vL=2\times \frac{22}{7}\times 50\times 0.7=220\Omega ]$

$=\frac{220}{220}=1or,\varphi ={45}^o$

Wattless component of current

$=I_0\sin \varphi =\frac{I_0}{\sqrt{2}}=\frac{1}{\sqrt{2}}.\frac{E_0}{Z}$

$=\frac{1}{\sqrt{2}}\frac{220}{\sqrt{X_L^2+R^2}}=\frac{1}{\sqrt{2}}.\frac{220}{\sqrt{{220}^2+{220}^2}}$

$=\frac{1}{2}=0.5A$