An inductor in an LC circuit has a maximum current of 2.2 A and a maximum energy of 60 mJWhen the current in the inductor is 1.1 A , what is the energy stored in the capacitor? U _____ mJ
We know that he energy in an LC circuit oscillates back and forth between the inductor and capacitor. When Vc(t) 0, VL(t) is at it's maximum and when VL(t) 0, Vc(t) is at it's maximum. At iLmax 2.2A all the energy is in L and there is no energy in C (Vc 0) Solve for L E ?Li? 0.06J -----L 0.12/2.2? 0.0248H 24.8mH We know that ?Li? + ?CV? 0.06J for all t Subtract the energy in L from the max energy to find the energy in C: ?CV? 0.06 - ?Li? 0.06 - ?(0.12/2.2?)*1.1? 0.045J 45mJ This makes sense because the energy in the inductor is proportional to i? 0.06*(1.1/2.2)? 0.06/4 0.015 J so when the current is half in L, the energy is 1/4 meaning the other 3/4 of the energy must be in the capacitor.
