1. I suppose, speaking about capacity, you've meant 1500u
F?
2. In the 1st formula the voltage has to be squared:
\[E=\frac{1}{2}\cdot{C}\cdot{V}^{2}\]
The result (its order) looks like you have squared the voltage but I don't understand its numerical value - I obtained 79.2J.
3. The resistor value is rather 12Ω (11.6Ω).
4. The
time constant for your 11Ω resistor is 16.5ms, for 12Ω resistor it is 18ms, so why do you think it is 20ms?
5. If your last formula were right (
it is not), the numerical value of its result would be 4125 W (using your strange results above) or (using the right results) 4801W (for 11Ω) or 4401W (for 12Ω). None of them corresponds to your 4560W... How come?
However, as I already mentioned above, the formula is wrong. Power (instant) is given as
\[{p} = \frac{\mathrm{d}E}{\mathrm{d}t }\]
Your formula is
valid only if the change of energy E is constant during time (and therefore also the instant power dissipated in
R would be constant during time in such a case), which is not true! Also the
t in your formula is not a time but the
time constant of the RC circuit; its common designation is
τ (greek tau, so that not to confuse it with time).
The current
i(
t), as a function of time, charging a capacitor
C through a resistor
R from a constant voltage source
V is given as:
\[{i(t)}={Imax}\cdot {{e}}^{-\frac{t }{RC}}=\frac{ {V}}{R }\cdot {{e}}^{-\frac{t }{RC}}\]
The corresponding instant power
p(
t) dissipated in resistor
R is then:
\[{p(t)}={R}\cdot {i(t)}^{2}=\frac{{ {V}}^{2 }}{R }\cdot {{e}}^{-\frac{2t }{RC}}\]
The maximum
instant power dissipated in
R is at
t=0, i.e.
pMAX =
V^2/
R = 8802W (if
R=12Ω).
This instant power decreases exponentially with the time constant
τ/2 =
RC/2,
so, for instance, after
τ=18ms it will be 1191W, after 3
τ=54ms it will be 21.8W and after 5
τ=90ms it will be 0.4W.