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Capacitance is a fundamental concept in understanding how capacitors operate. A capacitor is a device that stores electrical energy, with its ability to hold charge measured by its capacitance. This property is expressed as the ratio of the electric charge (Q) stored on each plate of the capacitor to the potential difference (V) across the plates. It is symbolized by the letter \( C \) and its unit is the Farad (F). In simpler terms, capacitance tells us how much charge a capacitor can store for a given voltage.
A larger capacitance means a capacitor can store more charge for the same voltage. In the exercise, a capacitance of \( 120 \mu \mathrm{F} \) means the capacitor can store \(120 \times 10^{-6} \mathrm{Coulombs} \) of charge per volt across its plates. This parameter becomes crucial when calculating other factors like potential difference and stored energy.

Potential difference, also known as voltage, is the difference in electric potential between two points in a circuit. It is what drives the flow of charge in a circuit, acting like a pressure that pushes electrons around. In terms of a capacitor, potential difference is the voltage across the two plates of the capacitor. It is influenced by the amount of charge stored on the plates and the capacitor's capacitance.
The potential difference is crucial because it indicates how much energy per charge is stored in the capacitor. A higher potential difference across a capacitor typically means that the capacitor is storing more energy. In our exercise, the voltage or potential difference was found to be approximately \(1103 \mathrm{V}\), calculated from the given energy and capacitance values using the potential energy formula.

The capacitor formula is key in understanding the relationship between energy, capacitance, and potential difference in a capacitor. The formula given as \( U = \frac{1}{2} C V^2 \) links these three critical pieces.
This equation shows that the electric potential energy \( U \), stored in a capacitor, is directly proportional to the capacitance \( C \) and the square of the potential difference \( V \). To find any of these quantities, you can rearrange the formula accordingly.
For example, to find \( V \) from the exercise, you rearrange to \( V^2 = \frac{2U}{C} \), and then solve for \( V \) by taking the square root. It's important to ensure all units are compatible—here, converting microfarads to farads was necessary.
This formula underlines the physical insights and calculations in problems involving capacitors, enabling us to determine how changes in one quantity (capacitor size, stored energy, or voltage) affect the others.