Question

A 450 uF capacitor is charged to 295 V. Then a wire is connected between the plates. How many joules of thermal energy are produced as the capacitor discharges if all of the energy that was stored goes into heating the wire?


I am totally confused I don't even know where to start. Help please!

Answer 1

Gee, I guess I better figure out how much energy is stored in a capacitor at voltage Vf and capacitance C
C = q/V
q = V C
dq/dt = i = C dV/dt
power = i V
power = C V dV/dt
so
power dt = C V dV
integral power dt = Energy = C integral V dV from V = 0 to V = Vf
but integral of x dx = (1/2)x^2 + constant
so
Energy at Vf = (1/2)C Vf^2
ok, now we can use that
Energy = (1/2)(450*10^-6)(295)^2
or
19.6 Joules