In series LCR circuit C =2 F , ~L =5 mH and R =5 . The ratio of energy stored in the inductor to that in capacitor, when maximum current flows through the circuit is

Step-by-step solution

Given: Series LCR circuit (C=2 ~F , L=5 mH , R=5 ) We are asked for the ratio of energy in inductor to that in capacitor when the current through the circuit is maximum → this happens at resonance. At resonance: - Impedance (Z=R ) - Let supply voltage be (V ) and current be (I ). Then (V=I R ) Energy stored in the inductor: (U_L= 1 2 L I^2 ) Energy stored in the capacitor (using (V=I R ) ): (U_C= 1 2 C V^2= 1 2 C(I R)^2 ) Hence, ( U_L U_C = 1 2 L I^2 1 2 C I^2 R^2 = L C R^2 ) Substitute values: ( gathered U_L U_C =