Question

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

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

Answer 1

The correct option is A $4.0A$

If $\omega =50\times 2\pi$ then $\omega L=20\Omega$
If ${\omega }^{\prime }=100\times 2\pi$ then ${\omega }^{\prime }L=40\Omega$
$I=\frac{200}{Z}\frac{200}{\sqrt{R^2+{\left({\omega }^{\prime }L\right)}^2}}=\frac{200}{\sqrt{{30}^2+{\left(40\right)}^2}}$
$I=4A$.