Question Video: Calculating the Energy Stored by a Capacitor

A capacitor has a charge of 2.5 𝜇C when connected to a 6.0-V battery. How much energy is stored in this capacitor?

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Video Transcript

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?

If we picture this capacitor as part of an electric circuit, it might look like this, connected to a battery with a 6.0-volt supply. We’re told that the charge 𝑄 on this capacitor is 2.5 microcoulombs. And knowing this as well as the potential difference across the capacitor, we want to solve for the energy stored in it. If we refer to this energy as capital 𝑈, then that’s given by one-half the charge on a capacitor times the potential difference across it.

Recalling further that the capacitance of the capacitor is equal to the charge on one of its plates divided by the potential difference across it, we can see that, thanks to this second expression, it’s possible to rewrite the energy on a capacitor in different ways. But the way we’ve written it here is a helpful way because it involves charge and potential difference, both of which we’ve been given in our problem statement. Calculating the energy 𝑈, we plug in 2.5 times 10 to the negative six coulombs for 𝑄 in 6.0 volts for 𝑉. Calculating this product, we find a result of 7.5 microjoules. That’s the energy stored in this capacitor.

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