In a series resonant LCR circuit the voltage across R is 100 volts and R = `1 k(Omega) with C =2(mu)F`. The resonant frequency `(omega)` is `200 rad//s`. At resonance the voltage across L is

Options

A. 100 V
B. 150 V
C. 200 V
D. 250 V

Answer

D

Explanation

At resnonace, `omegaL = 1/(omegaC) and Z = R`
Current through the circuit `I = (V_R)/(R) = 100/1000 = 0.1A`
`:.` Voltage across L is given by `V_(L) = IX_(L) = I omega L`
but `omega L = 1/(omega C)`
`:. V_(L) = 1/(omega C)`
`=(0.1)/(200 xx 2 xx 10^(-6)) = 1000/4 = 250V`.