Question

A coil has an inductance of $0.7\text{H}$ and is connected in series with a resistor of resistance $220\Omega$. When an alternating emf of $220\text{V}$ at $50\text{cycles/s}$ is applied to it, the wattless component of the current in the circuit is equal to

• A. $5\text{A}$
• B. $0.5\text{A}$
• C. $0.7\text{A}$
• D. $7\text{A}$

Answer 1

The correct option is B $0.5\text{A}$

Given:-
$L=0.7\text{H};R=220\Omega ;V=220\text{V}$

$f=50\text{Hz}$


Now, Inductive reactance
$X_L=\omega L=2\pi fL$

$X_L=2\pi \times 50\times 0.7$

$\Rightarrow X_L=219.9\Omega \approx 220\Omega$

Drawing the impedance triangle


$Z=\sqrt{{220}^2+{220}^2}=220\sqrt{2}\Omega$

As we know that,
$\tan \varphi =\frac{X_L}{R}=\frac{\omega L}{R}=\frac{220}{220}=1$

$\Rightarrow \varphi ={45}^{\circ }$

Now, current in the circuit

$I=\frac{V}{Z}=\frac{220}{220\sqrt{2}}=\frac{1}{\sqrt{2}}\text{A}$

Wattless component of current
$=I\sin \varphi$

$=\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=0.5\text{A}$

Hence, option $\left(\text{B}\right)$ is correct.

Concept:- Wattless current is the current in the circuit in which average power consumed by the circuit is zero.