Question

In an $R L C$ series circuit shown in figure, the readings of voltmeters $V_{1}$ and $V_{2}$ are $100 \,V$ and $120 \,V$, respectively. The source voltage is $130\, V$. For this situation, mark out the correct statement(s).

• A. Voltage across resistor, inductor and capacitor are $50 V$, $50 \sqrt{3} V$, and $120+50 \sqrt{3} V$, respectively
• B. Voltage across resistor, inductor, and capacitor are $50 V , 50 \sqrt{3} V$, 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} $
$\Rightarrow V_{ R }=50 \,V$
$\Rightarrow V_{ L }=\sqrt{100^{2}-50^{2}}=50 \sqrt{3} V$
$V_{ C }=120+50 \sqrt{3} V$
$\cos \phi=\frac{V_{ R }}{V}=\frac{50}{130}=\frac{5}{13}$
Since $V_{ c } < V_{ L }$, so circuit is capacitive.