Question

In an $RLC$ series circuit shown in figure, the readings of voltmeters $V_1$ and $V_2$ are $100V$ and $120V$, respectively. The source voltage is $130V$. For this situation, mark out the correct statement(s).

• A. Voltage across resistor, inductor and capacitor are $50V$, $50\sqrt{3}V$, and $120+50\sqrt{3}V$, respectively
• B. Voltage across resistor, inductor, and capacitor are $50V,50\sqrt{3}V$, and $120-50\sqrt{3}V$, respectively
• C. Power factor of the circuit is $\frac{5}{13}$
• D. The circuit is capacitive in nature

Answer 1

Answer: (A), (C), (D)

$V_R^2+V_L^2=100^2,\left|V_C-V_L\right|=120$

$130^2=V_R^2+{\left(V_C-V_L\right)}^2$
$\Rightarrow V_R=50V$
$\Rightarrow V_L=\sqrt{100^2-50^2}=50\sqrt{3}V$
$V_C=120+50\sqrt{3}V$
$\cos \varphi =\frac{V_R}{V}=\frac{50}{130}=\frac{5}{13}$
Since $V_c<V_L$, so circuit is capacitive.