Question

An arc lamp requires a direct current of $10\text{A}$ at $80\text{V}$ to function. If it is connected to a $220\text{V}\left(\text{rms}\right)$, $50\text{Hz}$ supply, the series inductor needed for it to work, is close to-

• A. $0.08\text{H}$
• B. $0.044\text{H}$
• C. $0.065\text{H}$
• D. $80\text{H}$

Answer 1

The correct option is C $0.065\text{H}$

Given, $I=10\text{A};V=80\text{V}$

$R=\frac{V}{I}=\frac{80}{10}=8\Omega$

For $\left(ac\right)$ source,

$V_{rms}=I{Z}_{req}$ $[Z=\text{Impedance}]$

$Z_{req}=\frac{220}{10}=22\Omega$

$Z^2=R^2+X_L^2$

$X_L=\sqrt{{22}^2-8^2}=20.49$

$\omega L=20.49$

$L=\frac{20.49}{2\pi \times 50}=0.065\text{H}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.