A 4.00-μF capacitor and a 6.00-μF capacitor are connected in parallel across a 600 -V supply lin

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A 4.00-μF capacitor and a 6.00-μF capacitor are connected in...

A $4.00-\mu \mathrm{F}$ capacitor and a $6.00-\mu \mathrm{F}$ capacitor are connected in parallel across a 600 -V supply line. (a) Find the charge on each capacitor and voltage across each. (b) The charged capacitors are disconnected from the line and from each other. They are then reconnected to each other with terminals of unlike sign together. Find the final charge on each capacitor and the voltage across each.

Key Concepts

Capacitors in Parallel

When capacitors are connected in parallel, they share the same voltage across their terminals because their corresponding plates are connected together. This means that if a voltage is applied, each capacitor will develop a charge based solely on its own capacitance according to the relation Q = C × V.

Charge-Voltage Relationship

The relation Q = C × V is fundamental in understanding capacitor behavior, stating that the stored charge (Q) on a capacitor is directly proportional to both the capacitance (C) and the voltage (V) across it. This principle is used to calculate the charge stored in capacitors when a known voltage is applied.

Conservation of Charge

In an isolated system where capacitors are disconnected from an external voltage source, the total charge is conserved. When capacitors are reconnected, even if their configuration changes, the final distribution of charge will adhere to the principle of charge conservation, ensuring that the overall net charge remains constant.

Capacitor Reconnection and Charge Redistribution

When previously charged capacitors are reconnected in a new configuration (such as connecting oppositely charged plates together), the charges redistribute between them until they reach a common voltage. The initial conditions and conservation of charge dictate the final distribution, and this process may result in a change of polarity if terminals of opposite charge are connected.

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