Question

A resistor and a capacitor are connected to an ac supply of $200V,50Hz$ in series. The current in the circuit is $2A$. If the power consumed in the circuit is $100W$ then the capacitance in the circuit is:

• A. $\frac{100}{100\pi }F$
• B. $\frac{25}{100\pi }F$
• C. $\frac{\sqrt{125\times 75}}{100\pi }F$
• D. $\frac{1}{100\pi \sqrt{125\times 75}}F$

Answer 1

The correct option is D $\frac{1}{100\pi \sqrt{125\times 75}}F$

$V_{rms}=200V$
$I_{rms}=2A$
$P=100=I_{rms}^{2}R=4R$
$R=25\Omega$
$\sqrt{R^2+X_C^2}=\frac{V_{rms}}{I_{rms}}=100$
$X_C=\sqrt{{100}^2-{25}^2}=\sqrt{9375}=\sqrt{125\times 75}$
$X_C=\frac{1}{C\omega }=\sqrt{125\times 75}$
$C=\frac{1}{\omega \sqrt{125\times 75}}=\frac{1}{2\pi 50\sqrt{125\times 75}}F$