How much energy is stored in a 12-microfarad capacitor whose plates are at a potential difference of 3.0 volts?
In this question, there are three quantities that we want to connect. Energy is one, capacitance is the other, and potential difference is the third. We can recall or look up a mathematical relationship that brings all three together. The energy stored in a capacitor, we can call it 𝑢, is equal to one-half multiplied by the capacitance of the capacitor 𝑐 times the potential difference across it squared.
When we apply this relationship to our scenario, we can say that the energy stored is equal to one-half 12 times 10 to the negative six farads times 3.0 volts squared. And calculating this value to two significant figures, we find it’s 54 microjoules. That’s how much energy a capacitor with this capacitance and potential difference has stored in it.