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

Q: A coil has an inductance of 0.7 H and is joined in series with a resistance of 220Ω. When an alternating emf of 220 V at 50 cps is applied to it, then the wattless component of the current in the circuit is (take 0.7π = 2.2)

(a) 5A

(b) 0.5A

(c) 0.7A

(d) 7A

Ans: (b)

Sol: Wattless component of current $\displaystyle = I_0 sin\phi$

$\displaystyle X_L = \omega L = 2\pi \nu L$

$\displaystyle X_L = 2 \pi \times 50 \times 0.7 = 222 ohm$

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

$\displaystyle Z = \sqrt{220^2 + 220^2 } = 220\sqrt{2}$

$\displaystyle I_0 = \frac{E_0}{Z} = \frac{220}{\sqrt{2} \times 220}$

$\displaystyle I_0 = \frac{1}{\sqrt{2}} A$

$\displaystyle tan\phi = \frac{X_L}{R} = 1$

φ = 45°

Wattless component of current $\displaystyle = \frac{1}{\sqrt{2}} sin45$

= 0.5 A