Circuits I · Capacitors, inductors, and first-order transients
Capacitors C_1=20 μF and C_2=30 μF are connected in series
Problem
Capacitors \(C_1=20\,\mu\mathrm{F}\) and \(C_2=30\,\mu\mathrm{F}\) are connected in series. Capacitor \(C_3=8.0\,\mu\mathrm{F}\) is connected in parallel with that series combination. The complete three-capacitor network is attached to a \(50\,\mathrm{V}\) independent DC voltage source and is left connected until every current has vanished. Isolated-node charge is only that required by electrostatic equilibrium. (a) Determine the equivalent capacitance presented to the source. (b) Determine the voltage and the charge of each of \(C_1\), \(C_2\), and \(C_3\). (c) Determine the energy stored in each capacitor and the total stored energy.
Hint
After all currents vanish the source voltage sits across the parallel combination; series capacitors then split that voltage.
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