Absence of any dissipation mechanism dooms a pure LCcircuit 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 ...
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