A parallel-plate capacitor is a device made from two conducting plates separated by an insulating gap. When charge is moved from one plate to the other, the plates store equal and opposite charges and create an electric field between them. Capacitors matter because they store electrical energy, control timing in circuits, filter signals, and help stabilize voltage.
The simple parallel-plate model is one of the clearest ways to see how geometry affects electrical behavior.
For ideal large plates, the electric field between the plates is nearly uniform, so the voltage difference is related to field strength by V = Ed. The capacitance increases when the plate area is larger, decreases when the plate separation is larger, and increases when a dielectric material is inserted between the plates. A dielectric reduces the effective electric field for the same free charge, allowing the capacitor to store more charge at the same voltage.
The stored energy can be described in several equivalent ways, including U = 1/2 CV^2.
Key Facts
- Capacitance is the charge stored per volt: C = Q/V.
- For an ideal air or vacuum parallel-plate capacitor: C = epsilon0 A/d.
- With a dielectric completely filling the gap: C = kappa epsilon0 A/d.
- The electric field between ideal plates is approximately uniform: E = V/d.
- For plates in vacuum with surface charge density sigma: E = sigma/epsilon0.
- Stored energy can be written as U = 1/2 CV^2 = 1/2 QV = Q^2/(2C).
Vocabulary
- Capacitance
- Capacitance is a measure of how much charge a capacitor stores for each volt of potential difference.
- Dielectric
- A dielectric is an insulating material placed between capacitor plates that increases capacitance by reducing the effective electric field.
- Electric field
- An electric field is the force per unit positive charge at a point in space.
- Surface charge density
- Surface charge density is the amount of charge per unit area on a surface, written as sigma = Q/A.
- Potential difference
- Potential difference is the energy transferred per unit charge between two points, measured in volts.
Common Mistakes to Avoid
- Using C = QV instead of C = Q/V is wrong because capacitance is charge per volt, not charge multiplied by voltage.
- Forgetting that increasing plate separation decreases capacitance is wrong because C = epsilon0 A/d shows that d is in the denominator.
- Assuming the electric field outside the plates is the same as inside is wrong because the ideal model gives a strong nearly uniform field between the plates and a much smaller fringing field outside.
- Treating a dielectric as a conductor is wrong because a dielectric polarizes but does not allow free charge to flow through it like a metal.
Practice Questions
- 1 A parallel-plate capacitor has plate area 0.020 m^2 and separation 1.0 mm in air. Using epsilon0 = 8.85 x 10^-12 F/m, find its capacitance.
- 2 A 4.0 microfarad capacitor is connected to a 12 V battery. Find the charge stored on each plate and the energy stored in the capacitor.
- 3 A capacitor remains connected to a battery while a dielectric slab is inserted fully between the plates. Explain what happens to the capacitance, charge on the plates, voltage, and stored energy.