Question

A coil has resistance $30\Omega$ and inductive reactance $200\Omega$ at $50\text{Hz}$ frequency. If an AC supply of $200\text{V},100\text{Hz}$ is connected across the coil, the current in the coil will be

• A. $6\text{A}$
• B. $10\text{A}$
• C. $4\text{A}$
• D. $8\text{A}$

Answer 1

The correct option is C $4\text{A}$

$R=30\Omega ;X_L=20\Omega$ at $f=50\text{Hz}$

Inductance, $L=\frac{X_L}{\omega }=\frac{X_L}{2\pi f}=\frac{20}{2\pi \times 50}=\frac{1}{5\pi }\text{H}$

$V_{rms}=200\text{V};f^{\prime }=100\text{Hz}$

$I_{rms}=\frac{V_{rms}}{Z}=\frac{V_{rms}}{\sqrt{R^2+X{{}_L}^2}}=\frac{V_{rms}}{\sqrt{R^2+(2\pi f^{\prime }L{)}^2}}$

Substituting the data given in the question,

$I_{rms}=\frac{200}{\sqrt{{30}^2+[2\pi \times 100\times \frac{1}{5\pi }{]}^2}}=\frac{200}{\sqrt{{30}^2+{40}^2}}$

$I_{rms}=\frac{200}{50}=4\text{A}$.

Hence, option (d) is the correct answer.