Capacitors

Introduction

A capacitor is a device designed to store electric charge. It consists of two parallel conducting plates spaced some small distance apart. Capacitors are used to store information in computer random access memory (RAM) or the energy needed to power a camera flash. The parallel plates can be small and single layered, leading to disk shaped devices, or the plates can be rolled together (with insulators preventing the plates from touching) to create cylindrical tubes.

In a simple capacitor there are two parallel plates with area A separated by some distance d. If the two plates are connected to the terminals of a battery, each plate will gain an equal, but opposite, charge such that the voltage between the plates is equal to the voltage between the battery terminals. The actual charge value each plate possesses is related to the voltage of the battery and the properties of the capacitor by the following equation: Q=CV

The variable, C, is the capacitance of the capacitor and depends on the area of the plates and their separation. We calculate capacitance using the equation: , where ε0 is the permittivity of free space = 8.85 x 10-12 C2/N•m2. Capacitance is measured in units of farads (F). 1 F is very large, so it is common to see capacitors with ranges of 1 picofarad (pF) to 1 microfarad (μF).

Note: You should notice that in the equation above we use V to represent potential difference (voltage) instead of ΔV. When solving problems using electric circuit components, like capacitors, this will be our standard.

The charged stored in the capacitor can be released, by design, for many different electrical purposes. We'll explore these more in the next unit.

Since capacitors store opposite charges on the two plates they store electrical energy. Depending on the information given, you can calculate this energy in the following ways:

Capacitance Practice

(a) Calculate the capacitance of a parallel-plate capacitor whose plates are 20 cm x 3.0 cm and are separated by a 1.0 mm air gap.

(b) What is the charge on each plate if a 12 V battery is connected across the plates?

(c) How much electric energy is stored in the capacitor when it is fully charged?

SOLUTIONS

You'll notice in the parallel plate capacitor above that the plates may not just be separated by air. To insulate the two plates a material known as a dielectric may be inserted between the plates. A dielectric does not allow electric charge to flow between the plates as easily. Changing the dielectric material can change the capacitance of the capacitor by the following equation:

, where K is the dielectric constant.

Some common dielectric constants include: Air = 1.00; Paper = 3.7; Glass = 5; Rubber = 6.7; Strontium Titanate = 300.

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