Question

An inductive circuit contains resistance of $1\Omega$ and an inductance of $2.0\text{H}$. If an $AC$ voltage of $120\text{V}$ and frequency $60\text{Hz}$ is applied to this circuit, the current would be nearly

• A. $0.8\text{A}$
• B. $0.48\text{A}$
• C. $0.16\text{A}$
• D. $0.32\text{A}$

Answer 1

The correct option is C $0.16\text{A}$

Given:

$R=1\Omega ;L=2.0\text{H};V_{rms}=120\text{V}$

$f=60\text{Hz}$

Now, $\omega =2\pi f=120\pi \text{rad/s}$

Now, inductive reactance,

$X_L=\omega L=240\pi \approx 753.6\Omega$

Impedence, $Z=\sqrt{R^2+X_L^2}$

Here, $X_L>>R$

So, $Z\approx X_L=753.6\Omega$

$\therefore i_{rms}=\frac{V_{rms}}{Z}=\frac{120}{753.6}\approx 0.16\text{A}$

Hence, option $\left(C\right)$ is correct.