Consider the RC circuit in the figure below. The switch was at position a for a long period and it is suddenly switched to position b at time t = 0.

http://s1.postimage.org/nqpr2v8yf/prob01a_rccircuit.gif

What is Vc at time t = 2.00 ms?
Use the following data : R = 452.5 Ω, C = 4.00 μF, Vb = 3.75 V.
1.242 V so yeah I did that :))

now , here is my problem with this question
What is the total energy dissipated by the resistor R after the switch is thrown?

what I did was
W= -(epsilon^2)*C/2
W= -2.8125*10^-5 J

and that is wrong!! What can I do ?

The resistor will eventually end up dissipating ALL of the energy stored within the capacitor. The energy storage of a capacitor is



which works out to the answer you got except for the minus sign (assuming the units for the capacitance were microfarads, that is. It's impossible to tell from your copy-and-paste).

Since the question is asking about energy dissipated, the answer should be positive. If the resistor was dissipating a negative amount of energy, that would be a double-negative, meaning that the resistor would be creating energy!