Capacitors C1=6.00 μF and C2=2.00 μF are charged as a parallel combination across a 250-V batter

step 1 So if we have two capacitors connected to a battery, 250 volts, and the capacitors are connected

Capacitors C1=6.00 μF and C2=2.00 μF are charged as a...

Capacitors $C_{1}=6.00 \mu \mathrm{F}$ and $C_{2}=2.00 \mu \mathrm{F}$ are charged as a parallel combination across a $250-\mathrm{V}$ battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to positive plate. Calculate the resulting charge on each capacitor.

Key Concepts

Charge Redistribution in Reconfigured Capacitor Networks

After initially charging capacitors in parallel, if they are disconnected from the battery and then reconnected in a different way (for example, by connecting the positive plate of one to the negative plate of the other), the charges on the individual capacitors will redistribute. This redistribution occurs until a common voltage is achieved across the capacitors, and the final charge on each capacitor can then be found using the relation Q = CV in conjunction with charge conservation principles.

Effect of Polarity in Capacitor Connections

The polarity with which capacitors are connected plays a crucial role in determining the resultant charge distribution. Connecting the positive plate of one capacitor to the negative plate of another effectively subtracts charges from the system, thereby impacting the net charge available for redistribution when the capacitors are reconnected. This concept is critical when analyzing circuits where the capacitors are reconfigured after being charged.

Capacitor Charge-Voltage Relationship

This concept is central to understanding capacitors. A capacitor’s ability to store charge is directly related to the voltage across it and its capacitance, as given by the equation Q = CV. This relationship is used both when the capacitor is being charged by an external voltage source and when it is left to redistribute its charge after being disconnected from that source.

Conservation of Charge

When capacitors that have been charged separately are connected together, the total charge in the system remains constant, assuming no external discharging paths or losses. In circuit reconfigurations such as connecting plates with opposite polarities, it is the conservation of charge that allows us to determine how the initial charges redistribute among the capacitors.

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