Question

a coil has resistance 30ohm and inductive reactance 20ohm at 50Hz frequency . if an AC source ,of 200V , 100Hz is connected across the coil, the current in the coil will be

1) 2A

2) 4A

3) 8A

Answer 1

$$\begin{gathered} X_l=20ohmwhenfrequencyis50Hz. \\ 2\pi fL=20 \\ 2\pi \times 50L=20 \\ L=\frac{1}{5\pi } \\ whenfrequencyis100Hz. \\ {X}_l=2\pi \times \frac{1}{5\pi }\times 100=40ohm \\ impedanceZ=\sqrt{R^2+{X_l}^2} \\ Z=\sqrt{900+1600} \\ Z=50ohm \\ V=200volt \\ I=\frac{200}{50} \\ I=4A. \end{gathered}$$