Capacitors

A capacitor is a device that stores electric charge and electric potential energy using two conductors separated by an insulator. It appears in circuits that smooth voltage, store energy briefly, filter signals, and control timing. The basic idea is simple: one plate gains positive charge, the other gains negative charge, and an electric field forms between them. Understanding capacitors helps students connect charge, voltage, energy, and electric fields in one system.

For a parallel plate capacitor, the amount of charge stored depends on the capacitance and the voltage across the plates. The electric field in the gap is related to the voltage and plate separation, and the stored energy depends on both capacitance and voltage. A dielectric placed between the plates changes how the field behaves and usually increases the capacitance. These relationships explain why capacitor geometry and material choice matter in real devices.

Key Facts

Capacitance is defined by C = Q/V.
For a parallel plate capacitor, C = epsilon A/d.
The electric field between ideal parallel plates is E = V/d.
Stored energy can be written as U = (1/2)CV^2.
Equivalent forms of capacitor energy are U = (1/2)QV and U = Q^2/(2C).
A dielectric increases capacitance by C = k epsilon_0 A/d, where k is the dielectric constant.

Vocabulary

Capacitance: Capacitance is a measure of how much charge a device stores per unit voltage.
Dielectric: A dielectric is an insulating material placed between capacitor plates that affects the electric field and usually increases capacitance.
Electric field: An electric field is the region where electric charges experience a force, and in a capacitor it points from the positive plate to the negative plate.
Potential difference: Potential difference, or voltage, is the electrical energy per unit charge between two points.
Parallel plate capacitor: A parallel plate capacitor is a capacitor made of two flat conducting plates separated by a small gap.

Common Mistakes to Avoid

Using Q = CV with mismatched units, which gives wrong answers because charge must be in coulombs, capacitance in farads, and voltage in volts.
Thinking the plates touch through the dielectric, which is wrong because the plates must remain separated by an insulator or gap to store charge properly.
Assuming a capacitor stores charge on only one plate, which is wrong because equal magnitude and opposite sign charges build up on both plates.
Using U = CV^2 instead of U = (1/2)CV^2, which doubles the stored energy and leads to a systematic calculation error.

Practice Questions

1 A capacitor has capacitance 5.0 microfarads and is connected to a 12 V battery. Find the charge stored on the capacitor.
2 A parallel plate capacitor has plate area 0.020 m^2 and plate separation 1.0 x 10^-3 m with air between the plates. Use epsilon_0 = 8.85 x 10^-12 F/m to calculate the capacitance.
3 A dielectric is inserted between the plates of an isolated charged capacitor. Explain what happens to the capacitance, the electric field, and the voltage across the plates.