# A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 Ω . When an alternating e.m.f of 220 V…

Q: A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 Ω . When an alternating e.m.f of 220 V at 50 cps is applied to it, then the wattles component of the current in the circuit is

Sol: $\large tan\phi = \frac{X_L}{R} = \frac{\omega L}{R}$

$\large tan\phi = \frac{2\pi \times 50 \times 0.7}{220} = 1$

φ = 45°

$\large Z = \sqrt{R^2 + X_L^2}$

$\large Z = \sqrt{220^2 + 220^2} = 220\sqrt{2} ohm$

Wattless component of current = Iv sinφ

$\large = \frac{E_v}{Z} sin45^o = \frac{220}{220 \sqrt{2}} \times \frac{1}{\sqrt{2}}$

= 0.5 A