Question

In a $R-L-C$ series circuit shown, the reading of voltmeter $V_1$ and $V_2$ are $100$ $V$ and $120$ $V$ respectively. Choose the correct statement.

• A. Voltage across resistor, inductor and capacitor are $60V,86.6V$ and $206.6V$ respectively
• B. Voltage across resistor, inductor and capacitor are $10V,90V$ and $30V$ respectively
• C. Power factor of the circuit is $\frac{5}{13}$
• D. Power factor of the circuit is $\frac{7}{13}$

Answer 1

The correct option is C Power factor of the circuit is $\frac{5}{13}$

${V^2}_R+{V^2}_L=10000....\left(i\right)$
$V_L-V_C=120....\left(ii\right)$
${V^2}_R+{\left(V_L-V_C\right)}^2={\left(130\right)}^2=16900....\left(iii\right)$
On solving
$V_R$= $50$ $V$, $V_L$=$86.6$ $V$, $V_C$=$206.6$ $V$
and $\cos \left(\varphi \right)=\frac{V_R}{V}=\frac{50}{130}=\frac{5}{13}$
As $V_{\underset{}{c}}>V_L,$circuit is capacitive in nature.