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Wize University Physics Textbook (Master) > DC Circuits

Energy Stored in a Capacitor

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Capacitors in Series and ParallelNext Section
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Energy Stored in a Capacitor


When charging a capacitor, charges are transferred to the two plates of the capacitor. The work done on these charges is stored as electric potential energy, which is given by:

 U=12Q2C=12CV2 \boxed{\ U=\dfrac{1}{2}\frac{Q^2}{C}=\dfrac{1}{2}CV^2\ }







The stored electric potential energy changes when charging or discharging the capacitor.


Exam Tip
A charged capacitor can act as the source of the energy in the circuit (discharging capacitor)

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Example: Double the Energy


Consider a parallel-plate capacitor that is connected to a battery. You want to double the energy stored in the capacitor by changing the spacing between the capacitor plates. How do you change the spacing?

The voltage is the same before and after since the capacitor is always connected to the battery.

The capacitance is given by:

C=κεoAdC=\dfrac{\kappa\varepsilon_oA}{d}

Let's substitute this into the energy formula:

U=12CV2U=\dfrac{1}{2}CV^2

=12 κεoAd V2=\dfrac{1}{2}\ \dfrac{\kappa\varepsilon_oA}{d}\ V^2


Therefore, the energy and the distance an inversely proportional. So if we want double the energy, we should have half the distance: d→d2d\to\dfrac{d}{2}

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Practice: Changing Area and Spacing


Consider a parallel plate capacitor that is connected to a battery. The plate separation is dd, the area each plate is AA. The capacitor has charge QQ, capacitance CC, energy UU, and voltage VV.

You cut the area of each plate in half, and then reduce the spacing to a third of the original value. What effect does this have on:

a) the voltage across the capacitor?
b) the capacitance?
c) the charge stored by the capacitor?
d) the energy stored by the capacitor?

e) Repeat parts (a) to (d) if the capacitor is first disconnected from the battery and then its area and spacing change the same way.

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Electric Energy Density

The electric energy density is defined as the total energy per volume and it is given by:

 uE=UV \boxed{ \ u_E=\dfrac{U}{V} \ }

  • uEu_E is the electric energy density (energy per unit volume)
  • UU is the total electric energy stored in the capacitor
  • VV is the volume of the system


For a planar capacitor this becomes:
 uE=UdA=12ε0E2 \boxed{ \ u_E=\frac{U}{dA}=\frac{1}{2}\varepsilon_0 E^2 \ }


  • AA is the area of the plates
  • dd is the distance between the plates
  • ε0\varepsilon_0 is the permittivity of free space, ε0=8.854×10−12\varepsilon_0=8.854\times10^{-12} F/m
  • EE is the electric field inside the capacitor


Practice: Electric Energy Density


A capacitor has a charge of 22 µC stored on its plates. The area of each plate is 2020 mm2. Find the electric energy density for this capacitor.