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

E=\frac 1 2 CV^2

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!