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.
