An isolated capacitor of unknown capacitance has been...

An isolated capacitor of unknown capacitance has been charged to a potential difference of $100 \mathrm{~V}$. When the charged capacitor is disconnected from the battery and then connected in parallel to an uncharged $10.0-\mu \mathrm{F}$ capacitor, the voltage across the combination is measured to be $30.0 \mathrm{~V}$. Calculate the unknown capacitance.

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Key Concepts

Capacitance

Capacitance is a measure of the ability of a system to store electric charge per unit voltage. It is quantified by the ratio of the charge stored on the capacitor to the voltage across it and is fundamental in analyzing how capacitors behave in circuits.

Capacitors in Parallel

When capacitors are connected in parallel, they all experience the same voltage across their terminals. The total or equivalent capacitance of capacitors in parallel is the sum of their individual capacitances, which is a key concept when analyzing charge distribution in a circuit after connection.

Conservation of Charge

Conservation of charge is the principle that the total electric charge in an isolated system remains constant over time. In capacitor circuits where capacitors are connected after being charged or discharged, this principle ensures that the sum of the charges before connection equals the sum after connection.

Voltage (Potential Difference)

Voltage, or electric potential difference, is the measure of energy difference per unit charge between two points. In the context of capacitors, the voltage across a capacitor is directly related to its stored charge and capacitance, making it crucial for analyzing how energy is redistributed when capacitors are connected.

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