Discharging a Capacitor: Calculating Energy Dissipation

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The discussion centers on calculating the energy dissipated by a 25Ω resistor when a 0.25μF capacitor charged to 50V discharges through it and a 100Ω resistor. Initial calculations incorrectly assume constant power output of 100W for the 25Ω resistor, neglecting the time-varying nature of current and voltage during discharge. Participants suggest integrating instantaneous power over time to accurately determine total energy dissipation, rather than relying on a single power value. The importance of using both P = V²/R and P = I²R is emphasized for a complete analysis. Ultimately, the correct approach involves understanding the changing dynamics of the circuit during capacitor discharge.
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Homework Statement


A 0.25μF capacitor is charged to 50V. It is then connected in series with a 25Ω resistor and a 100Ω resistor and allowed to discharge completely. What is the energy dissipated by the 25Ω resistor in Joules?

Homework Equations


I'm assuming I need:
P=V^2/R
I(t)=I0*e^-(t/τ)
τ=RC

The Attempt at a Solution


So I used P=V^2/R to get that the power output of the 25Ω resistor is 100W. Then all I need is the time to find out how much energy was released. I know I cannot solve I(t) for when it is 0 without getting ∞. So I calculated the time it would take for the capacitor to be at an I=.01(I0), got a t=1.43*10^-4 secs. Then multiplying by the power, I got an energy release of .0144 J which is not correct. I'm not sure how else I would do this.
 
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apamirRogue said:

Homework Statement


A 0.25μF capacitor is charged to 50V. It is then connected in series with a 25Ω resistor and a 100Ω resistor and allowed to discharge completely. What is the energy dissipated by the 25Ω resistor in Joules?

Homework Equations


I'm assuming I need:
P=V^2/R
I(t)=I0*e^-(t/τ)
τ=RC

The Attempt at a Solution


So I used P=V^2/R to get that the power output of the 25Ω resistor is 100W. Then all I need is the time to find out how much energy was released. I know I cannot solve I(t) for when it is 0 without getting ∞. So I calculated the time it would take for the capacitor to be at an I=.01(I0), got a t=1.43*10^-4 secs. Then multiplying by the power, I got an energy release of .0144 J which is not correct. I'm not sure how else I would do this.

Surely the power dissipated by the resistors changes over time, since the current and hence the voltage drops change over time. So "100W" for the 25Ω resistor doesn't seem to be meaningful.

You might also want to take note of the fact that while P = V2/R, it is also P = I2R.

e0 = 1, so there's no problem solving for I when t = 0.

You should think about integrating the instantaneous power over time to find the total energy.
 

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