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Homework Statement
I think I have a solution to this but I might have made a logical error so I want to check if my reasoning works.
You have two capacitors one charged by some unspecified mean to a paricular voltage. It is connected then connected to another capacitor in parallel with resistor somewhere in the loop. What is the heat dissipated through the resistor?
Homework Equations
v = v0 * e^(-t/RC) discharging capacitor
P = V^2/ R heat dissipation through resistor
C = Q/V
The Attempt at a Solution
Charge is conserved in the situation so regardless of the capacitor eventually the potential difference of the 2 capacitors is the same
Q = C1V1
VFinal = Q/(C1+C2)
We can find the time it took for the orginal capacitor to discharge the amount need to reduce the potential difference to Vfinal namely
t = -RC * ln(vf/v0)then we can look at the infinetessimal amount of heat disappainted at each time
dW = V(t)^2/R dt
then you take the integral from 0 to t as shown and get some number.
I see a potential problem with this though. Since the given potential at time t is that of the capacitor do I instead of to use the current through the resistor at time t and then integrate over dW = I(t)^2/R dt?
Also I feel like I'm discounting whatever changes to the current/ potential to the wire will happen as a result of capacitor 2 charging. I feel that since I know the amount of charge that moved through the resistor I should just easily be able to calculate the energy loss. What principle am I missing?
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