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. 40V
B. 250V
C. `4 xx 10^(-3) V`
D. `2.5 xx 10^(-2) V`

Answer

B

Explanation

Here `V_R = 100V, R = 1k Omega = 10^3 Omega , C = 2mu F = 2 xx 10^(-6) F, omega = 200 rad//s `
Current , `I = V/Z `, where `V = sqrt((V_R)^2 + (V_L - V_C)^2)`
` Z = sqrt(R^2 + (X_L - X_C)^2)`
At resonance , ` X_L = X_C therefore Z = R`
`V_L = V_C therefore V = V_R`
` therefore I = (V_R)/(R ) = (100V)/(10^3 Omega) = 10^(-1) A`
At resonance , `V_L = V_C = IX_C = (I)/(omega C)`
` = (10^(-1))/(200 xx 2 xx 10^(-6) ) = (10^3)/(4) = 250 V`