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AP® Physics C: E & M

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Difficult

Charging Capacitor in a Circuit

APPHEM-3GDZE9

A Circuit contains a resistor of resistance $\mathit{R}$ and a capacitor $C_1$ of capacitance $\mathit{C}$, a second Capacitor $C_2$ of capacitance $\mathit{2C}$, and a battery that provides an emf of $V$, as shown above.

Initially, both switches are open and both capacitors are uncharged. At time $t=0$, switch 1 is closed. What is the charge as a function of time?

A

The charge is constant but not zero

B

Zero

C

$Q(t)=Ct$

D

$Q(t)=VCe^{\frac{1}{RC}(Q-VC)t}$

E

$Q(t)=VC(1- e^{\frac{1}{RC}(Q-VC)t})$