Question

A $50W$, $100V$ lamp is to be connected to an AC mains of $200V,50Hz$. What capacitor is essential to be put in series with the lamp?

• A. $\frac{25}{\sqrt{2}}\mu F$
• B. $\frac{50}{\pi \sqrt{3}}\mu F$
• C. $\frac{50}{\sqrt{2}}\mu F$
• D. $\frac{100}{\pi \sqrt{3}}\mu F$

Answer 1

The correct option is B $\frac{50}{\pi \sqrt{3}}\mu F$

for $100V,50W$lamp , $R=\frac{{100}^2}{50}=200\Omega$
capacitor put in series should be such that,
$V_R=\frac{R}{\sqrt{R^2+X_C^2}}{V}_s=100$
$\Rightarrow \frac{1}{C\omega }=X_C=\sqrt{3}R$
$C=\frac{1}{\omega \sqrt{3}R}=\frac{50}{\pi \sqrt{3}}\mu F$