Question

Initially, the switch in the figure (Figure 1) is in position A and capacitors C2 and C3 are uncharged. Then the switch is flipped to position B. Afterward, what are the charge on and the potential difference across EACH capacitor if V=100 Volts?

Answer 1

Initially, charge on C1 is q = CV = 100 * 15 = 1500 uC

Also, the combined capacitance of C2 and C3 in series is 20*30/(20+30) = 12 uF

When the switch is flipped, we know two things:

potential across the 2-3 combo is the same as the final potential of C1 (because they are in parallel), and the total charge is still 1500 uC

So...

total charge = 15 * V + 12 * V = 1500

V = 55.556 Volts

Charge remaining on C1 = CV = 15 * 55.556 = 833.33 uC

C2 and C3 each have charge = 12 * 55.556 = 666.67 uC

and potential of C2 = q/C = 666.67 / 20 = 33.33 Volts

potential of C3 = 666.67 / 30 = 22.22 V

in summary

C1: final charge 833.33 uC, final potential 55.56 V

C2: final charge 666.67 uC, final potential 33.33 V

C3: final charge 666.67 uC, final potential 22.22 V