In the shown circuit, capacitors 1 and 2 each have capacitance C. When dielectric K is inserted into capacitor 1, find the total charge that flows through the battery.
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Question

In the shown circuit, capacitors 1 and 2 each have capacitance C. When dielectric K is inserted into capacitor 1, find the total charge that flows through the battery.

G1 Physics · Accepted Answer

Initially two equal capacitors in series have equivalent C/2. After insertion they become KC and C in series, equivalent KC/(K+1). The change in battery charge is E[KC/(K+1)−C/2]=(K−1)CE/[2(K+1)]. Its direction for the shown polarity is from C to B. Correct answer: D.