Question

A coil has resistance $30\Omega$ and inductive reactance $20\Omega$ at 50 Hz frequency. If an ac source, of 200 V, 100 Hz is connected across the coil, the current in the coil will be:

• A. $\frac{20}{\sqrt{1}3}A$
• B. 2.0 A
• C. 4.0 A
• D. 8.0 A

Answer 1

The correct option is C 4.0 A

According to the problem,

frequency is $50Hz$ when,

$X_l=20\Omega$

$2\pi fL=20$

$2\pi \times 50L=20$

$L=\frac{1}{5\pi }$

If the frequency is $100Hz$,

$X_l=2\pi \times \frac{1}{5\pi }\times 100=40\Omega$

Impedance $Z$,

$Z=\sqrt{R^2+{X_l}^2}$

$Z=\sqrt{900+1600}$

$Z=50\Omega$

$V=200volt$

$I=\frac{200}{50}$

$I=4A$