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Hi there.

I'm trying to evaluate the energy dissipated due to Joule effect on a resistor within an RC circuit

(R, C, and battery in series), with the capacitor initially uncharged.

Till now I just came up with the formula for the current flowing in the circuit

[itex]i(t) = e^{-\frac{t}{RC}}[/itex], resulting from a differential equation.

The energy dissipated by the resistance should be the power over R integrated from 0 to ∞:

[itex]\displaystyle E = \int_0^\infty P(t)dt = \int_0^\infty e^{-\frac{t^2}{(RC)^2}}dt[/itex]

which appears to be something I just can't calculate.

I'm quite sure there's a simpler way to do this.. do yo have any hint?

I'm trying to evaluate the energy dissipated due to Joule effect on a resistor within an RC circuit

(R, C, and battery in series), with the capacitor initially uncharged.

Till now I just came up with the formula for the current flowing in the circuit

[itex]i(t) = e^{-\frac{t}{RC}}[/itex], resulting from a differential equation.

The energy dissipated by the resistance should be the power over R integrated from 0 to ∞:

[itex]\displaystyle E = \int_0^\infty P(t)dt = \int_0^\infty e^{-\frac{t^2}{(RC)^2}}dt[/itex]

which appears to be something I just can't calculate.

I'm quite sure there's a simpler way to do this.. do yo have any hint?

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