Question

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

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

Answer 1

The correct option is A $\text{4.0 A}$

Given:
Resistance $R=30\text{ohm}$
inductive reactance $X_L=\text{20 Ohm}$ at $\text{50 Hz}$
ac source, $V=\text{200 volt, f=100 Hz}$,

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