- #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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