- #1
squelch
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Homework Statement
For the circuit shown, the ##\varepsilon## has negligible resistance. Initially the capacitor is uncharged and the switch S is in position 1. The switch is then moved to position 2, so that the capacitor begins to charge.
Given: [R, C, E]
Find:
The energy given to the circuit by the battery from t=0 to t=infinity.
Homework Equations
See attempt at a solution.
The Attempt at a Solution
After a long time, I know that the charge on the capacitor is ##Q=CV=C\varepsilon##.
As a function of time, I'm aware that [itex]q = Q(1 - {e^{\frac{{ - t}}{{RC}}}})[/itex]
I know that [itex]P = {I^2}R = \frac{{{V^2}}}{R}[/itex] but I also know that current does not flow through a capacitor, so I'm at a bit of a loss as to how to calculate power here. I'm imagining that I must set up an integral relating to the time constant above from t=0 to t=infinity, but I'm not quite sure how to set up the integral.
For voltage as a function of time, I came up with [itex]1 - \frac{q}{{C\varepsilon }} = {e^{\frac{{ - t}}{{RC}}}}[/itex]
For current as a function of time, I came up with [itex]\frac{q}{{CR(1 - {e^{\frac{{ - t}}{{RC}}}})}} = I[/itex]
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