The Mystery of Capacitors Charge
What happens when capacitors with different capacitance and charges are connected in series?
A 3.0-µF capacitor charged to 40 V and a 5.0-µF capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 3.0-µF capacitor?
Answer:
The final charge on the 3.0-µF capacitor is 90 µC.
When capacitors with different capacitance and charges are connected in series, they share the same charge. In this case, the final charge is determined by the capacitance of the capacitors and the voltage they are charged to.
Using the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, we can calculate the charge on the 5.0-µF capacitor first. The charge on the 5.0-µF capacitor is:
Q = (5.0 µF)(18 V) = 90 µC.
Since capacitors connected in series share the same charge, the final charge on the 3.0-µF capacitor will also be 90 µC. This is because the charge is conserved in a series circuit.