# Capacitors in a circuit

1. Jan 1, 2018

### Eitan Levy

1. The problem statement, all variables and given/known data

C1=C2=C3=C
No internal resistance.
We wait for a while and the put a dielectric material in C3. Then after waiting again we remove the voltage source and after that we take this material out. How will the voltages on the capacitor be affected?

2. Relevant equations
CV=Q

3. The attempt at a solution
I just don't understand how to know what will change and how to know what will happen in the circuit after that. I know that the voltage on C3 will be affected, but from there how to know what will happen to the other capacitors? What would give us a balanced circuit?

2. Jan 1, 2018

### kuruman

If you can calculate all the voltages before and after the dielectric is inserted, you can compare and see what is different. Once you know the voltages, you can find the charge on each capacitor. Once the battery is disconnected, will the capacitors lose their charges? What about after the dielectric is removed with the battery still disconnected? Remember, the total charge stays the same because it has nowhere to go after the battery is disconnected.

3. Jan 1, 2018

### Eitan Levy

I understand the total stays the same, but how am I supposed to know if each capacitor's charge will be changed? Maybe because the voltages are not identical on each capacitor, it will change? I have no idea how to figure this out.

4. Jan 1, 2018

### kuruman

What happens to the capacitance of C3 when the dielectric is inserted with the battery still connected? Does it change or does it stay the same?

5. Jan 1, 2018

### Eitan Levy

It changes, the voltage changes and it's charge stays the same.

6. Jan 1, 2018

### kuruman

How do these changes occur? What increases and what decreases? Can you find V3 and Q3 before the dielectric is inserted? What about after the dilectric is inserted?

7. Jan 1, 2018

8. Jan 1, 2018

### Eitan Levy

I can find them before. After I am not sure how to.

9. Jan 1, 2018

### Eitan Levy

10. Jan 1, 2018

### kuruman

You mean after the dielectric is removed with the battery disconnected? Yes, current will flow so that the new charge on C3 is the same as on the parallel combination.

11. Jan 1, 2018

### Eitan Levy

I thought it stays the same anyway?

12. Jan 1, 2018

### Staff: Mentor

Can you clarify this? When the voltage source is removed, is the circuit left open where the source was or is the source replaced by a short circuit (a wire) to close the gap?

13. Jan 1, 2018

### Eitan Levy

It is replaced by a wire I believe.

14. Jan 1, 2018

### kuruman

The answer will be different if the battery is replaced with a wire as opposed to when it is not.

15. Jan 1, 2018

### Eitan Levy

I understand , but it doesn't say specifically what happened, just that the voltage source was removed.
According to the answers only the voltage on C3 will change, maybe you can understand from this?

16. Jan 2, 2018

### Eitan Levy

Can anyone help me out with this? I just have an exam tomorrow so I am pretty nervous.

17. Jan 2, 2018

### Delta2

If only the voltage on $C_3$ changes then when the battery is removed leaves open circuit. Because if it was shorted with wire then essentially as you can verify the circuit becomes 3 capacitors in parallel so if voltage in one changes then voltage in all changes since they all have same voltage.

18. Jan 2, 2018

### Eitan Levy

So if we put a wire where we took out the voltage source, current would have flown right? (Because V3=2ε/3 and V12=ε/3).

19. Jan 2, 2018

### Staff: Mentor

Yes. It might be instructive to look at the charges on the capacitors: Make a circuit drawing showing the distribution of charges on the capacitor plates in the instant before the battery-replacing wire is inserted.

20. Jan 2, 2018

### Delta2

yes and if the connecting wire has zero resistance the current that will flow it will be infinite but will last only for infinitesimal time dt. The total charge that will flow from/into the C_3 capacitor will be finite Idt=infinite * 0=finite for this case.