The power supply in a stereo receiver contains a \(2500-\mu \mathrm{F}\) capacitor charged to 35 V. How much energy does it store?

Understanding capacitance conversion is crucial when working with capacitors in various electronics. Capacitors are essential components that store electrical energy in an electric field. The standard unit for capacitance is the farad (F), which represents a large capacitance in practical terms. This is why we often deal with smaller units like microfarads (\textmu F), nanofarads (nF), or picofarads (pF).

Converting from one unit to another involves multiplying or dividing by powers of 10. For instance, 1 microfarad is equivalent to one millionth of a farad, or \(1 \times 10^{-6}\) F. To convert from microfarads to farads, you multiply the value in microfarads by \(1 \times 10^{-6}\). This step is essential to align the units before using them in formulas for calculations, ensuring accurate results.

Knowing how to calculate the energy storage of a capacitor is a useful skill in electronics. The energy (E) stored in a capacitor is calculated using the formula:
\[E = \frac{1}{2} C V^{2}\]
where

• \(C\) is the capacitance in farads, and
• \(V\) is the voltage across the capacitor in volts.

This formula derives from the work done to charge the capacitor. The factor of \(\frac{1}{2}\) appears because the capacitor charges to its maximum voltage gradually, not instantaneously, and on average, only half of the applied voltage is used throughout the charging process.

When executing the calculation (like in our stereo receiver example), it's crucial to ensure all values are in the correct units (farads for capacitance and volts for voltage). After converting the units and substituting into the formula, the result gives the energy stored in joules (J), the unit of energy in the International System of Units (SI).

Electric potential energy is the energy that is needed to move a charge within an electric field. In the context of a capacitor, this energy is what we calculate when we want to know how much energy the capacitor is capable of storing. This energy is directly related to the voltage, representing the potential difference, or 'pressure', that can cause charges to move, and the capacitance, which is a measure of how much charge the capacitor can hold at a specific voltage.

The conversion of electrical energy into electric potential energy, and vice versa, is fundamental in electronic devices, such as saving power when needed or smoothing out fluctuations in power supply. The key takeaway is that a capacitor's ability to store electric potential energy makes it indispensable in electronic circuits for various applications like filtering, timing, and transient suppression.