A 2.20 µF capacitor (#1) is charged to 942 V and a 6.41 µF capacitor (#2) is charged to 657 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each and the charge on each? [Hint: Charge is conserved.] It wants final charge and final voltage
To determine the final potential difference across each capacitor and the final charge on each capacitor, we need to apply the principle of charge conservation.
When the positive plates of the capacitors are connected to each other and the negative plates are connected to each other, the capacitors are essentially connected in parallel. In this configuration, the potential difference across each capacitor will be the same, while the charges on each capacitor will add up.
Let's denote the potential difference across the capacitors as V and the charges on the capacitors as q1 and q2. Initially, capacitor #1 has a potential difference of 942 V and a capacitance of 2.20 µF, so its initial charge can be calculated using the formula q1 = C1 * V1:
q1 = (2.20 µF) * (942 V) = 2068.4 µC
Similarly, capacitor #2 has an initial potential difference of 657 V and a capacitance of 6.41 µF, so its initial charge is given by q2 = C2 * V2:
q2 = (6.41 µF) * (657 V) = 4211.37 µC
When the capacitors are connected in parallel, the charges add up, so the total charge Qtot is given by:
Qtot = q1 + q2 = 2068.4 µC + 4211.37 µC = 6280.77 µC
Since the capacitors are in parallel, the potential difference V across each capacitor will be the same. To find this common potential difference, we can rearrange the equation q = C * V to V = q / C:
V = Qtot / (C1 + C2) = 6280.77 µC / (2.20 µF + 6.41 µF) ≈ 696.32 V
Therefore, the final potential difference across each capacitor is approximately 696.32 V. The final charge on capacitor #1 will remain the same as its initial charge, which is 2068.4 µC. The final charge on capacitor #2 will remain the same as its initial charge, which is 4211.37 µC.