In an L-C-R series AC circuit the voltage across L,C and R is 10 V each. IF the inductor is short circuited , the voltage across the capacitor would become

Options

A. 10V
B. `20/sqrt2V`
C. `20sqrt2V`
D. `10/sqrt2V`

Answer

D

Explanation

Circuit is resonant, hence supply voltage equals to `V_R`.
`V_R=10` volt
Also, `X_C=R`
As the voltage drops are equals across L,C and R then when L is short
`Z=sqrt(R^2+X_C^2)`
`=sqrt2 R`
`V_c=iX_c[ because i=V/Z]`
or `V_c=V/Z X_c`
or `=10/(sqrt2 R) R`
or `V_C=10/sqrt2` volt