A 20-μF capacitor charged to 2.0 kV and a 40-μF capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 20-μF capacitor after the two are so connected?
A) 53 mC
B) 27 mC
C) 40 mC
D) 80 mC
E) 39 mC

Question

Quizplus · Accepted Answer

When the capacitors are connected, charge redistributes until the voltage across both capacitors is equal. The total initial charge is conserved. The initial charges are Q1 = 20μF * 2000V = 40mC and Q2 = 40μF * 3000V = 120mC. The total charge is 160mC. The equivalent capacitance is 60μF. The final voltage is 160mC / 60μF = 2.67kV. The final charge on the 20μF capacitor is 20μF * 2.67kV = 53.4mC, but since the capacitors are connected with opposite polarities, the charge on the 20μF capacitor is 40mC - 13.4mC = 26.6mC, approximately 27mC.

A 20-μF Capacitor Charged to 2