Electric Circuits and Networks, Ist Edition by Pearson

Absence of any dissipation mechanism dooms a pure LC circuit with non-zero

energy storage to oscillate forever. But suppose there is a little resistance in series – so

little that there is no marked change in the shape of v

C

(t) and i(t) in the first cycle.

However, in that case, the current which flows through the resistance must dissipate some

energy cycle after cycle (however minute that may be) leading to reduction of the total

available stored energy in the circuit. And, that must surely lead to gradual loss of

amplitude of voltage and current oscillation. Sometime or other the circuit must settle

down to a zero-energy state.

Therefore, we throw ...