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!
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
No problem, I can help you with that! To find the amount of thermal energy produced as the capacitor discharges, there are a few steps we can follow.
First, let's determine the initial energy stored in the capacitor. The energy stored in a capacitor is given by the formula:
E = 0.5 * C * V^2
where E represents the energy stored, C is the capacitance, and V is the voltage.
Substituting the given values:
E = 0.5 * (450 x 10^-6 F) * (295 V)^2
Now let's calculate the value of E.
E = 0.5 * (450 x 10^-6) * (295)^2
Simplifying this expression will provide us with the initial energy stored in the capacitor.
Once we have the initial energy, we can assume that all of it goes into heating the wire. The formula to calculate the thermal energy produced is:
Thermal energy = E
Since we already calculated the initial energy E, we can use that value to find the amount of thermal energy produced.
Now, let's substitute the calculated value of E into the formula to find the thermal energy.
The thermal energy produced = E
If you perform the calculations as explained, you will find the answer in joules.