Question

A acapacitor of capacitance C has initial charge Q and connected to an inductor of inductance L. At t=0 switch S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is​

Answer 1

The current would be 0.5Q/sqrt(LC)

• Initially,
• energy of the capacitor = 0.5Q^2/C
• energy of the inductor = 0.5Li^2

• According to the question, energy contained in the capacitor is equal to the energy of the inductor when energy on capacitor becomes three times
• i.e., 3[0.5Li^2] + 0.5Li^2 = 0.5Q^2/C
• ⇒ (3/2)Li^2 + 0.5Li^2 = 0.5Q^2/C
• ⇒ 2Li^2 = 0.5Q^2/C
• ⇒ i^2 = 0.25 Q62/(LC)
• ⇒ i = 0.5Q/sqrt(LC)