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