Question

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

• A. $\frac{20}{\sqrt{13}}A$
• B. $2.0A$
• C. $4.0A$
• D. $8.0A$

Answer 1

The correct option is C $4.0A$

Given,

$X_L=20\Omega$

frequency $f=50Hz$

So, $2\pi fL=20$

$\Rightarrow 2\pi \times 50L=20\Rightarrow L=\frac{1}{5\pi }$

When the frequency is $100Hz$

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

Impedance $Z=\sqrt{R^2+X_L^2}=\sqrt{900+1600}=50\Omega$

$V=200volt$

Thus the current $I=\frac{200}{50}=4A$