Q: A 0.21 H inductor and a 12 ohm resistance are connected in series to a 220 V , 50 Hz ac source. Calculate the current in the circuit and the phase angle between the current and the source voltage.

Sol: Here ; X_{L} = ω L = 2π f L = 2π × 50 × 0.21 = 21π Ω

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

$\large Z = \sqrt{12^2 + (21 \pi)^2}$

$\large = \sqrt{144 + 4348}$

≈ 67 Ω

$\large I = \frac{V}{Z} = \frac{220}{67} $

= 3.28 A

$\large tan\phi = \frac{X_L}{R} = \frac{21 \pi}{12}$