Write down a differential equation that describes the behavior of the RC circuit shown below. The equation should describe the voltage change (dV/dt) as a function of the applied current (I). Arrange the equation such that the term (dV/dt) is alone on the left-hand side of the equation and all of the other terms are on the right.
Define i_R as the current through the resistor,
i_C as the current through the capacitor,
I as the total current, and V as the voltage drop.
|Current conservation dictates:||I = i_R + i_C||(1.1)|
|The resistive current is give by Ohm's law:||I_R = V/R||(1.2)|
|The capacitive current is give by:||i_C = C (dV/dt)||(1.3)|
|Substituting (1.2)-(1.3) into (1.1)||I = (V/R) + C (dV/dt)||(1.4)|
|Rearranging (1.4) to solve for dV/dt:||dV/dt = -V/(RC) + I/C||(1.5)|
|dV/dt = -V/(RC) + I/C|
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