An isolated capacitor C₁ carries a charge Q₀. Its wires are then connected to those of a second capacitor C₂, previously uncharged. What charge will each carry now? What will be the potential difference across each?

Verified step by step guidance

1. Start by understanding the principle of charge conservation. When the two capacitors are connected, the total charge in the system remains constant because no charge is lost or gained. This means the total charge before connection (Q₀) is equal to the total charge after connection.
2. Recognize that after the capacitors are connected, they will share the charge and reach the same potential difference (V) because they are connected in parallel. Use the relationship between charge, capacitance, and potential difference: Q = C × V.
3. Let the charges on the two capacitors after connection be Q₁ (on C₁) and Q₂ (on C₂). From charge conservation, we know Q₀ = Q₁ + Q₂.
4. Since the potential difference across both capacitors is the same after connection, use the formula V = Q₁ / C₁ = Q₂ / C₂. Rearrange this to express Q₂ in terms of Q₁: Q₂ = (C₂ / C₁) × Q₁.
5. Substitute Q₂ = (C₂ / C₁) × Q₁ into the charge conservation equation Q₀ = Q₁ + Q₂. Solve for Q₁ and Q₂ in terms of Q₀, C₁, and C₂. Finally, use V = Q₁ / C₁ or V = Q₂ / C₂ to find the potential difference across each capacitor.

Key Concepts

Capacitance

Capacitance is the ability of a capacitor to store charge per unit voltage, defined as C = Q/V, where C is capacitance, Q is charge, and V is voltage. It is measured in farads (F) and indicates how much electric charge a capacitor can hold at a given voltage. Understanding capacitance is crucial for analyzing how capacitors behave when connected in circuits.

Charge Conservation

Charge conservation is a fundamental principle stating that the total electric charge in an isolated system remains constant. When two capacitors are connected, the charge from the charged capacitor will redistribute between them, ensuring that the total charge before and after the connection remains the same. This principle is essential for determining the final charge on each capacitor.

Voltage Division

Voltage division refers to the distribution of voltage across components in a circuit, particularly in series connections. When capacitors are connected, the voltage across each capacitor can be different, depending on their capacitance values. The final potential difference across each capacitor can be calculated using the relationship between charge, capacitance, and voltage, which is vital for solving the given problem.