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Capacitors and Capacitance

Electromagnetism

A capacitor is a component that stores electric charge and energy in an electric field. It charges up quickly, holds its charge, and can release it in a sudden burst.

What a capacitor is

A capacitor is usually two conducting plates separated by an insulator called a dielectric. When it is connected to a battery, one plate gains electrons and becomes negative while the other loses electrons and becomes positive, building up an electric field between the plates. The amount of charge stored per volt is the capacitance, measured in farads, symbol F. One farad is a very large capacitance, so most practical capacitors are measured in microfarads or picofarads. Capacitance grows with larger plate area and smaller separation, and inserting a dielectric material between the plates increases it further. Once charged, a capacitor keeps its charge until it is discharged through a circuit.

Storing energy

Charging a capacitor takes work, because each extra charge must be pushed against the repulsion of the charge already there. That work is stored as energy in the electric field between the plates, equal to one half times capacitance times voltage squared. When the capacitor discharges, that energy is released, often much faster than a battery could release the same energy. This is why a capacitor can power a camera flash: it charges slowly from a battery, then dumps its energy through the flash tube in a fraction of a second. In a circuit, a capacitor blocks steady direct current once charged, but lets alternating current pass by charging and discharging repeatedly.

Where you see it

Capacitors smooth the output of power supplies, removing the ripple left after alternating current is rectified. They time circuits, such as the flashing of a turn signal, because a capacitor charges and discharges at a predictable rate through a resistor. They tune radios by forming a resonant circuit with an inductor, selecting one frequency. Touchscreens sense the tiny change in capacitance when a finger approaches, and defibrillators store a large charge and release it in a single pulse to restart a heart. In each case the key property is the same: fast storage and release of electrical energy.

Common mistakes

• Saying a capacitor stores current: it stores charge and energy, not a flow of current.
• Using Q = CV with the wrong voltage: V is the voltage across the capacitor itself.
• Forgetting that capacitance does not depend on charge or voltage: for a given capacitor, C is fixed by its geometry and dielectric.

Practice questions

1. A 20 microF capacitor is charged to 6.0 V. What charge does it store?
   Show answer

   Q = CV = (20 x 10^-6) x 6.0 = 1.2 x 10^-4 C = 120 microC.

2. How much energy does that capacitor store?
   Show answer

   U = 0.5 x (20 x 10^-6) x 36 = 3.6 x 10^-4 J.

3. If the voltage across a capacitor doubles, what happens to its charge and energy?
   Show answer

   Doubling V doubles Q, and energy scales with V^2, so energy becomes 4 times larger.

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