Question

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

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

Answer 1

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

For a given coil

R:Resistance$=30\Omega$

$X_L:$ Inductive Reactance $=\omega L\Omega =\left(2\pi F\right)L\Omega$

At $50㎐,X_L=20\Omega$

$\therefore 2\pi \times 50\times L=20$

$\therefore L=\frac{20}{100\pi }$

At $100㎐$

$X_L=2\pi \times 100\times L=2\pi \times 100\times \frac{20}{100\pi }=40\Omega$

At $100㎐$

$z=impedance=\sqrt{R^2+{X_L}^2}$

$\therefore Z=\sqrt{{40}^2+{30}^2}=50\Omega$

Current at $200V,100㎐$ is given as

$I=\frac{V}{z}=\frac{200}{50}=4A$

Therefore option A is correct