Capacitors in Parallel and in Series — Question 1

Question 1

Parallel branches share voltage while their terminal charges add

Ideal capacitors C1=3.00 nF and C2=6.00 nF are connected in parallel across 12.0 V, starting uncharged.

1. Derive and calculate the equivalent capacitance and branch charges.

2. If C2 is disconnected while C1 remains attached to the source, find the retained charge on each isolated or connected capacitor, neglecting switch capacitance.

Question 1 - Solution

Parallel branches share voltage while their terminal charges add

(a) Method and calculation

$$Q_{\mathrm{total}}=C_1V+C_2V\Rightarrow C_{\mathrm{eq}}=C_1+C_2=9.00\,\mathrm{nF}.$$$$Q_1=36.0\,\mathrm{nC},\quad Q_2=72.0\,\mathrm{nC},\quad Q_{\mathrm{total}}=108\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$Q_{1,f}=C_1V=36.0\,\mathrm{nC}.$$$$Q_{2,f}=Q_{2,i}=72.0\,\mathrm{nC},\quad V_{2,f}=Q_{2,f}/C_2=12.0\,\mathrm V.$$

Physical check

Disconnection alone does not discharge an ideal capacitor; charge remains on its separated terminals.