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A 25 uF and a 40 uF capacitor are charged by being connected across separate 50 V batteries. The capacitors are then disconnected from their batteries and connected to each other, with each negative plate connected to the other positive plate. What is the final charge on each capacitor, and what is the final potential difference across the 40 uF capacitor?

I know capacitance is given by C = Q/V.

1) I find the charge initially on the 25 uF and 40 uF capacitors (call them C1 and C2, respectively) to be 1250 uC and 2000 uC.

2) The plates are now connected, so there must be some movement of charge.

3) I take the difference of these charges (for some reason I don't know) and find Qtotal = 750 uC. This is apparently the net charge. Why?

4) Since the voltage is constant on both (again, why?), I find

Q1/C1 = Q2/C2 => Q1 = (C1/C2)Q2

Qtotal = Q1 + Q2 = (C1/C2)Q2 + Q2 = Q2(C1/C2 + 1) => Q2 = Qtotal/(C1/C2 + 1) = 426 uC.

5) Therefore Q1 = Qtotal - Q2 = 288 uC.

6) The potential difference across the 40 uF capacitor (C2) is then Q2/C2 = 11.6 V

In particular, I don't understand how we found the net charge. I don't understand why we set the voltage of each capacitor equal to each other in step (4) but then find something different in step (6)

I know capacitance is given by C = Q/V.

1) I find the charge initially on the 25 uF and 40 uF capacitors (call them C1 and C2, respectively) to be 1250 uC and 2000 uC.

2) The plates are now connected, so there must be some movement of charge.

3) I take the difference of these charges (for some reason I don't know) and find Qtotal = 750 uC. This is apparently the net charge. Why?

4) Since the voltage is constant on both (again, why?), I find

Q1/C1 = Q2/C2 => Q1 = (C1/C2)Q2

Qtotal = Q1 + Q2 = (C1/C2)Q2 + Q2 = Q2(C1/C2 + 1) => Q2 = Qtotal/(C1/C2 + 1) = 426 uC.

5) Therefore Q1 = Qtotal - Q2 = 288 uC.

6) The potential difference across the 40 uF capacitor (C2) is then Q2/C2 = 11.6 V

In particular, I don't understand how we found the net charge. I don't understand why we set the voltage of each capacitor equal to each other in step (4) but then find something different in step (6)

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