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)

$tan \,\phi = \frac{X_{L}}{R} = \frac{\omega L}{R} = \frac{2\pi×50×0.7}{220} = 1$
$\Rightarrow \quad\phi = 45^{\circ}$ and $Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{220^{2} + 220^{2}} = 220 \,\sqrt{2}\,\Omega$
Wattles component of current $= I_{\upsilon}\, sin\phi$
$= \frac{E_{\upsilon}}{Z}sin\,45^{\circ } = \frac{220}{220\sqrt{2}} \times \frac{1}{\sqrt{2}} = 0\cdot5\,A$