Question: Amazingly, these electrical components know calculus! Starting from the equation ER(t) + Ec(t) = Ein(t), dq and since the capacitor current is the rate of

Amazingly, these electrical components know calculus! Starting from the equation ER(t)

Amazingly, these electrical components know calculus! Starting from the equation ER(t) + Ec(t) = Ein(t), dq and since the capacitor current is the rate of change of its charge: I(t) it , you get RI(t) + q(t) - Ein (t) Rat + cq(t) = Ein (t). In general you can write down a DE for any electrical circuit. As you include more components the DE will get more complicated, but if you stick to resistors, inductances and capacitors, then the equations will always be linear but of very high order. Problem 3. An RC-circuit with a 10 resistor and a 10-6F capacitor is driven by a voltage Ein(t) = sin(100t) V. If the initial capacitor voltage is zero, determine the current /(t) and the subsequent resistor and capacitor voltages. (5 points)

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