Question

A coil has an inductance of $0.7$ henry and is joined in series with a resistance of $220\Omega$. When an alternating emf of $220V$ at 50 cycles per second, is applied to it, then wattless component of current in the circuit is

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

Answer 1

Answer: (D)

Here, $X_L=\omega L=2\pi \cup L=2\pi \times 50\times 0.7=220\Omega$
$R=220\Omega$
$Z=\sqrt{R^2+X_L^2}=\sqrt{220^2+220^2}=220\sqrt{2}\Omega$
$I_{rms}=\frac{V_{rms}}{Z}=\frac{220V}{220\sqrt{2}\Omega }=\frac{1}{\sqrt{2}}A$
$\sin \varphi =\frac{X_L}{Z}=\frac{220}{220\sqrt{2}}=\frac{1}{\sqrt{2}}$
Wattless current $=I_{rms}\sin \varphi =\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=\frac{1}{2}A=0.5A$