Question

1. (a) Consider the LC circuit discussed in class, comprised of one inductor and one capacitor in a loop. There are no external sources, and the circuit is driven by its initial conditions. Prove that the energy stored in the circuit is a constant. (b) Now add a resistor in series with the inductor and capacitor. Prove that the energy in the circuit goes to 0 at t -+ oo.

Answer 1

L de C dt 7 C 2 + d2 -Qu Sin ot uhre Tatal eay 2 2 Co wt +asiwt Q2 Ca t + 1 2 F

+ VR t -o Ldi LR+ L d2 R ol C LC dt df2 ,2 1 4 2 A e wt B Sin wat3 + hne wd R2 4 L2

R aWSin (wa t) e Caau t &xR a4 To tal Emey LU t 2 10 2 2 Ce ot t dns Total emey -