How Does a Capacitor's Energy Change Over Time?

[ninjadrummer8]

Homework Statement

Questions 1-2:
Switch is ON and left for a very long time.
1) current in circuit after this time
2) energy in capacitor after this time

Questions 3-4:
Capacitor then hooked up to resistor.
3)Energy after another long time.
4)What happens to the energy that was in the capacitor before it was hooked up to the resistor.

Homework Equations

U = 1/2 CV^2

The Attempt at a Solution

1) current is 0 because after the capacitor is fully charged no current flows
2)just solve using U=1/2CV^2
3)Energy = 0 because capacitor would be discharged
4)energy goes into heat

I'm not sure about all these answers... can someone let me know if my thought process is correct? Thanks for any help!

 

[Hootenanny]

Looks okay to me.

 

[nlightner]

Your thought process is generally correct, but there are a few things to clarify.

1) After the switch is left on for a very long time, the current in the circuit will eventually reach 0. However, in the short term, there will still be a current flowing as the capacitor charges up. The current will decrease as the capacitor gets closer to being fully charged, but it will not immediately drop to 0.

2) The energy in the capacitor after a long time will be the maximum amount that the capacitor can hold, which is given by U = 1/2 CV^2. However, it's important to note that this energy is not constant - it will decrease as the capacitor discharges.

3) After being hooked up to a resistor, the capacitor will discharge and the energy stored in it will decrease. The amount of energy left in the capacitor after a long time will depend on the resistance of the circuit and the capacitance of the capacitor.

4) The energy that was in the capacitor before it was hooked up to the resistor will be converted into heat as the capacitor discharges. This is because the resistor will offer some resistance to the flow of current, and this resistance will cause some of the electrical energy to be converted into heat energy.

Overall, your thought process is on the right track. Just keep in mind that the capacitor will not immediately reach a fully charged or discharged state, and the energy stored in it will change over time as it charges or discharges.