electric circuits

bos1234 · Riemann Hypothesis Offline Joined: 24 Jan 2007 Posts: 449

Given the voltage drops for a resistor and capacitor are $E_R = iR$ and $E_c = \frac {1}{c}\int{i.dt}$ respectively, show that an RC-circuit with resistance R, capacitance C, voltage E and current i has equation $R.\frac {di}{dt} + \frac {1}{c}i = \frac {dE}{dt}$

how to proof this formula?

**Posted:** Thu Oct 23, 2008 6:45 pm

HilbertThm90

The sum across the voltage is 0 ("The Loop Law" I believe its called, that's not important really).

Thus $E-E_R-E_C=0$ or $E-iR-\frac{1}{c}\int i dt=0$ .

Take the derivative with respect to time to get $\frac{dE}{dt}-\frac{di}{dt}R-\frac{i}{c}=0$ . Now rearrange terms.

**Posted:** Thu Oct 23, 2008 8:14 pm

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