Question

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

• A. $100\Omega$
• B. $25\Omega$
• C. $\sqrt{125\times 75}\Omega$
• D. $400\Omega$

Answer 1

Answer: (C)

$\sqrt{125\times 75}\Omega$

$V_{rms}=200V$
$I_{rms}=2A$
$P=100=I_{rms}^{2}R=4R$
$R=25\Omega$

$\therefore X_C=\sqrt{R^2+X_C^2}=\frac{V_{rms}}{I_{rms}}=100$

$\Rightarrow X_C=\sqrt{{100}^2-{25}^2}=\sqrt{9375}=\sqrt{125\times 75}\Omega$