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Capacitance is a measure of a capacitor's ability to store electric charge per unit of voltage across its plates. It's analogous to a water tank's capacity; the larger the capacity, the more water it can hold at a certain pressure. The unit for capacitance is the farad (F), named after the English physicist Michael Faraday.

In our example, we are given a capacitance of 165 microfarads (\(165 \times 10^{-6}\text{F}\)). A capacitor with higher capacitance can store more charge at the same voltage, or it can store the same amount of charge at a lower voltage. It's important to understand that the capacitance of a capacitor is fixed by its physical attributes, such as the surface area of the conducting plates and the distance between them, as well as the type of dielectric material used.

It should also be clarified that when we convert from microfarads to farads, we're not really changing the capacitance but are simply expressing it in a different unit for easier calculation. For instance, in electronic circuits, microfarads and picofarads are commonly used because farads would be impractically large values for most applications.

Voltage, also referred to as electric potential difference, is a measure of the potential energy per unit charge between two points in an electric field. Imagine climbing a hill; the higher you go, the more gravitational potential energy you gain. Similarly, charge gaining electric potential energy is like it climbing to a higher voltage.

Role of Voltage in Capacitors

In the context of capacitors, voltage determines how much energy the capacitor can store. Specifically, the energy stored in the capacitor increases with the square of the voltage (as seen in the energy formula, which involves the voltage squared). This is why a small increase in voltage can lead to a much larger increase in stored energy.

The voltage applied to the capacitor in our problem is 119 volts (V). It is crucial to handle voltage with care, as too much voltage can lead to the breakdown of the dielectric material between the plates, potentially causing the capacitor to fail.

Electric potential energy can be thought of as the energy that is stored in an electric field due to the positions of charges. The potential energy in a capacitor is a result of the separation of charges on the two plates, with one plate holding a positive charge and the opposite plate holding an equal amount of negative charge.

The energy stored in a capacitor, as given by the formula \( E = \frac{1}{2} CV^2 \), tells us that this energy is half the product of the capacitance and the square of the voltage. This relationship is quadratic, indicating that a doubling of the voltage results in a quadrupling of the energy stored. Thus, even small capacitors can store significant amounts of energy if the voltage is high.

Calculating Electric Potential Energy

In the exercise, once the values are plugged into the formula and the calculation is performed, the result is an electric potential energy of approximately 1.17 Joules. This value is significant because it quantifies the amount of work that could be done, for instance, by releasing the stored charge through a circuit. The energy stored in a capacitor can be used in various applications, such as powering a motor or stabilizing power supply in electronic devices.