In an RLC series circuit shown in fig. the reading of voltmeters `(V_1) and (V_2)` are 100 V and 200 V respectively. The source voltage is 130 V. for this situation, mark out the correct statements (s).

Options

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 corcuit is `5/13`
D. The circuit is capactive in nature

Answer

A, C, D

Explanation

`V_(R )^(2)+V_(L)^(2)=100^(2), |V_(C )-V_(L)|=120`

`130^(2)=V_(R )^(2)+(V_(C )-C_(L)^(2) implies V_(R )=50V`
`implies (V_L)=sqrt(100^(2)-50^(2))=50 sqrt(3)V`
`V_(C )=120 + 50 sqrt(3) V`
`cos phi =(V_R)/(V) = (50)/(130)=(5)/(13)`
Since `(V_C) lt (V_L)`, so circuit is capacitive.