Question

A coil has an inductance of 0.7H and is joined in series with a resistance of 220 $\Omega$ . When an alternating e.m.f. of 220V at 50 c.p.s. is applied to it, then the wattless component of the current in the circuit is

• A. 5 ampere
• B. 0.5 ampere
• C. 0.7 ampere
• D. 7 ampere

Answer 1

Answer: (B)

0.5 ampere

Impedance of the circuit is given by:

$Z=\sqrt{R^2+(2\pi fL{)}^2}$

$Z=\sqrt{{220}^2+(2\pi \times 50\times 0.7{)}^2}$

$Z\approx 220\sqrt{2}\Omega$

Power factor is given by:

$\cos \varphi =\frac{R}{Z}=\frac{\pi }{4}$

Total current in the circuit flowing is:

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

Wattless component of current in the circuit is:

$I_a=I\sin \left(\varphi \right)$

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