A capacitor has a charge of 2.5 microcoulombs when connected to a 6.0-volt battery. How much energy is stored in this capacitor?
We can name the charge amount 2.5 microcoulombs 𝑄 and the potential difference across the battery 6.0 volts 𝑉. We want to know how much energy is stored in this capacitor, an amount will call 𝑢.
To start on our solution, we can recall the mathematical equation for the energy stored in the capacitor. That energy 𝑢 is equal to one-half the charge 𝑄 stored in a capacitor squared divided by the potential difference across the two capacitor plates. So 𝑢 equals one-half 𝑄 squared over 𝑉 or using our values one-half times 2.5 times 10 to the negative sixth coulomb squared divided by 6.0 volts.
Plugging these values into our calculator, we find that to two significant figures 𝑢 is 7.5 times 10 to the negative sixth joules or 7.5 microjoules. That’s how much energy is stored in this capacitor.