- #1
bornofflame
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Homework Statement
1. A 2.01 uFcapacitor that is initially uncharged is connected in series with a 6.51 kΩ resistor and an emf source with 74.6 V and negligible internal resistance. The circuit is completed at t = 0.
b) At what value of t is the rate at which electrical energy is being dissipated in the resistor equal to the rate at which electrical energy is being stored in the capacitor.
Given/Known:
##C = 2.01\cdot10^{-6} ~F##
##Q_0 = 0 ~C##
##R_1 = 6.51\cdot10^3 ~\Omega##
##\mathcal {E} = 74.6 ~V## (The source can be treated as ideal.)
##P = 854 mW## (From the prior part of the question.)
Homework Equations
##P = Wt##
##W = \frac 1 2 CU^2##
##U = \frac 1 2 CV^2##
The Attempt at a Solution
Using the relevant equations to solve for W:
##W = \frac 1 2 C U^2 = \frac 1 2 C\cdot (\frac 1 2 C V^2)^2 = \frac 1 8 C^2 V^4##
Plugging in numbers gives me: ##W = 31.4\cdot10^{-12}~J##
Then using ##W = Pt## to solve for ##t: t = \frac W P##, I get ##t=27.2\cdot10^{10}~s = 27.2 ~Gs##
This seems obviously wrong, I don't know exactly how many seconds it would take but this looks to be grossly out of proportion. I'm sure that the reason is because I'm not applying the equation for work properly but I'm not sure exactly what I am missing.