Question

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

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

Answer 1

Answer: (B)

$tan\varphi =\frac{X_L}{R}=\frac{\omega L}{R}=\frac{2\pi \times 50\times 0.7}{220}=1$
$\Rightarrow \varphi =45^{\circ }$ and $Z=\sqrt{R^2+X_L^2}=\sqrt{220^2+220^2}=220\sqrt{2}\Omega$
Wattles component of current $=I_{\upsilon }sin\varphi$
$=\frac{E_{\upsilon }}{Z}sin45^{\circ }=\frac{220}{220\sqrt{2}}\times \frac{1}{\sqrt{2}}=0\cdot 5A$