RC Circuit Energy Problem

1. The problem statement, all variables and given/known data
The switch in the figure below has been in position a for a very long time. It is suddenly flipped to position b for 1.65 ms, then back to a. How much energy is dissipated by the 50 Ω resistor? (Assume = 65 V.)

2. Relevant equations
ΔVloop = 0 Volts
Q/V = C
V = IR

3. The attempt at a solution
I understand that if the 125 Ω resistor wasn’t there, the capacitor would have the full 65 Volts across it, but there is a voltage drop across the 125 Ω resistor, so the capacitor has less than 65 Volts on it.

I set up an equation starting from the bottom left corner of the circuit, 0 = 65 Volts – (125 Ω)*I – Q/(20μF), and I tried to solve it by bringing the Q/(20μF) to the other side and replacing I with V/R, but the V in V/R is the voltage across the resistor, not the battery’s voltage.

In short, I’m stuck.


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