Consider the long-term (t>>>0) situation. initially the current is very small (c

Question

Consider the long-term (t>>>0) situation. initially the current is very small (compared to the max later achieved).

a. what is the long term current that flows?
b. what is the long term potential across C?
c. in the long term will the current approach the limit in a monotonic or oscillating fashion? why or why not?

Consider an R- 500-2 resistor, an L0.5H inductor, a battery E with an r = 5-Q internal resistance, & a capacitor C 500 MF. Before time t 0, the switch S is connected to A so that C charges up to a final steady value of O-100uC At exactly 0 the switch S is thrown to B, and B. the capacitor starts to discharge.

Explanation / Answer

a. In the long term the current will approach 0. This is because, the finite energy in the capacitor will be dissipated as heat in the resistor over multiple cycles.

b. Long term potential across C is 0, since the current is 0.

c. The long ter current will approach in an oscillating fashion. This is becasue, initially the capacitor will lose energy while discharging, but simultaneously charging the inductor which gains energy. Once the inductor beccmes dominant, its polarity revereses in accordance with Lenz law, charging the capacitor in the opposite direction. Once the inductor discharges, the capacitor starts discharging in the opposite directions thereby reversing the direction of the current. This process conntinues, but each time the amplitude gradually reducces to 0.

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