In series LCR circuit C = 2 uF, L=1 mH and R= 10 . What is the ratio of energies stored in the capacitor and inductor when maximum current flows through circuit?

Step-by-step solution

For a series LCR circuit undergoing free oscillations, the voltage equation is given by: V_L + V_R + V_C = 0 L di dt + iR + V_C = 0 When the current i in the circuit is maximum, its rate of change is zero, i.e., di dt = 0 . Substituting this into the voltage equation, we get: 0 + i_ max R + V_C = 0 V_C = -i_ max R The energy stored in the capacitor at this instant is: U_C = 1 2 C V_C^2 = 1 2 C (i_ max R)^2 The energy stored in the inductor at the same instant is: U_L = 1 2 L i_ max ^2 The ratio of the energy stored