An LCR series circuit is under resonance. If `I_(m)` is current amplitude, `V_(m)` is voltage amplitude, R is the resistance, Z is the impedance, `X_(L)` is the inductive reactance and `X_(C )` is the capacitive reactance, then

Options

A. `I_(m)=(Z)/(V_(m))`
B. `I_(m)=(V_(m))/(X_(L))`
C. `I_(m)=(V_(m))/(X_(C ))`
D. `I_(m)=(V_(m))/(R )`

Answer

D

Explanation

Impedance of the circuit, `Z=sqrt(R^(2)+(X_(L)-X_(C ))^(2))` At resonance, `X_(L)=X_(C )`
`therefore Z=R therefore I_(m)=(V_(m))/(Z)=(V_(m))/(R )`.