Final Charge on Connected Capacitors

What is the final charge on the 3.0-µF capacitor after it's connected to the 5.0-µF capacitor?

Answer:

The final charge on the 3.0-µF capacitor after it's connected to the 5.0-µF capacitor is 78.75 µC.

In this scenario, we have a 3.0-µF capacitor initially charged to 40 V and a 5.0-µF capacitor initially charged to 18 V. These capacitors are then connected to each other such that the positive plate of each is connected to the negative plate of the other. When capacitors are connected in series, the charges combine to reach a common voltage.

The initial charges on the capacitors can be calculated using the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. The 3.0-µF capacitor has an initial charge of 3.0 µF * 40 V = 120 µC, while the 5.0-µF capacitor has an initial charge of 5.0 µF * 18 V = 90 µC.

After connecting the capacitors, charge will redistribute until a common voltage is reached. The total charge when the capacitors are connected is 120 µC + 90 µC = 210 µC, and the total capacitance is 3.0 µF + 5.0 µF = 8.0 µF. By applying the formula Q = CV, we can calculate the common voltage to be 210 µC / 8.0 µF = 26.25 V.

Finally, we can determine the final charge on the 3.0-µF capacitor by substituting the common voltage back into the formula Q = CV. This gives us 3.0 µF * 26.25 V = 78.75 µC, which is the final charge on the 3.0-µF capacitor after being connected to the 5.0-µF capacitor.