Amateur Radio Manual/Ohm's Law and Resistors

This chapter is an overview of resistors and their practical concerns. Resistors are fundamental building blocks of amateur radio, being used for current limiters, voltage dividers, oscillators, filters and more.

Resistors

 * Resistors, generally speaking, resist the flow of electricity. They prevent some electrons from travelling through them. This means that current flow is reduced. Almost all materials have resistance (some, such as superconductors, have zero resistance.)
 * At an atomic level, resistors oppose the flow of electrons. Some compounds have only a moderate hold on their electrons. Thus, electricity can flow, but with less energy. These compounds are said to have a high resistance. Copper has a very loose hold on some of its electrons, which can consequently have its electrons dislodge with very little energy. Thus, copper has a low resistance.
 * The unit of resistance is the Ohm, named after Georg Ohm. An Ohm is the unit of resistance that will allow one Ampere to flow if an electromotive force of one Volt is applied. The symbol for an Ohm is a capital omega (Ω).

Practical Resistors
Two important things to know about resistors when using them are their schematic symbols and the resistor color code.






 * Fixed resistors, as the name implies have a fixed resistance.
 * Potentiometers have a variable resistance

The Resistor Value Color Code


A resistor generally has four color bands. The first two bands give the first two digits e.g. brown, black represents "10". The third band indicates the multiplier. This is merely the number of zeros you add to the end of the first two digits. For example, black, brown, red represents "10" "00", or "1000 Ω" or "1 kΩ".

Construction Techniques
There are three main construction techniques used in making resistors: wirewound, carbon composition, and metal film.


 * Wirewound
 * As explained in this book about resistors, the narrower a conductor, the higher its resistance. Also, the longer it is, the higher its resistance. Combining these two characteristics, a wirewound resistor consists of a long, thin wire wrapped in a coil. This creates a high resistance.
 * Pros
 * Can be made to very close tolerances (tolerance is how close the actual value is to the listed value)
 * High power handling capability
 * Cons
 * Bulky
 * Expensive
 * Highly inductive
 * Carbon Composition
 * This resistor consists of a carbon powder in a container with wires attached to it. Its resistance can be changed when manufactured by using different concentrations of carbon in the powder.
 * Pros
 * Very cheap
 * Non-inductive
 * Cons
 * Poor tolerance
 * Poor stability (i.e. the value of the resistor can change considerably with time)
 * Metal Film
 * This resistor consists of a container with a thin metal film on it. Its resistance at manufacture can be changed by etching the metal away in certain patterns.
 * Pros
 * Inexpensive
 * Non-inductive
 * Cons
 * If stressed beyond their limits, metal film resistors tend to stop conducting entirely rather than have their resistance changed. This is often a benefit, as in some cases no operation is preferable to unpredictable operation.

Ohm's Law
Ohm's Law a fundamental principle in electronics. The law states the relationship between electromotive force, current and resistance. Knowing any two of these allows the third one to be discovered. It is expressed as "E = IR", where E is the electromotive force in Volts, I is the current in Amperes, and R is the resistance in Ohms.

Consider the following two examples.

Examples
Answer:
 * 1) The voltage and resistance are known. The current must be found. From Ohm's Law, $$\mathrm{I} = \frac{\mathrm{E}}{\mathrm{R}} = \frac{12 \mathrm{V}}{1 \Omega} = 12 \mathrm{A}$$
 * No.

Answer:

From Ohm's Law, $$\mathrm{R} = \frac{\mathrm{E}}{\mathrm{I}} = \frac{5 \mathrm{V}}{2.5 \mathrm{mA}} = 2 \mathrm{k\Omega}$$

Notice in this case that milliamps were used instead of Amps. We are allowed to do this because we used kilohms as the unit of resistance ( 1 mA = 0.001 A).

Series and Parallel Combinations of Resistors


This image shows a schematic of two resistors in series. This is a series arrangement because the resistors are aligned head to tail; the current going through one resistor goes through both. The two most important aspects of this circuit are

where $$\mathrm{I_\mathrm{tot}}$$ is the total current and $$\mathrm{E_\mathrm{tot}}$$ is the total voltage
 * 1) $$\mathrm{I_\mathrm{tot} = I_1 = I_2}$$
 * 2) $$\mathrm{E_\mathrm{tot} = E_1 + E_2}$$

The current and voltage equations are determined from Kirchhoff's laws.



This image shows a schematic of two resistors in parallel. This is a parallel arrangement because the tails of the resistors are connected to each other and the heads are connected to each other. The two most important aspects of this circuit are:

where $$\mathrm{I_\mathrm{tot}}$$ is the total current and $$\mathrm{E_\mathrm{tot}}$$ is the total voltage
 * 1) $$\mathrm{E_\mathrm{tot} = E_1 = E_2}$$
 * 2) $$\mathrm{I_\mathrm{tot} = I_1 + I_2}$$

Once again, the current and voltage equations are determined from Kirchhoff's laws.

Effective Resistance of Series and Parallel Combinations
The effective resistance of combinations of resistors can be determined by Ohm's Law. In the serial case, $$\mathrm{E_\mathrm{tot}} = \sum_n{E_n}$$, while $$\mathrm{I_\mathrm{tot}}=\mathrm{I}_n$$ for all n. Since $$\mathrm{E}_n=I\times \mathrm{R}_n$$, $$\mathrm{E_\mathrm{tot}} = \sum_n{I\times R_n} = I\sum_n{R_n}$$. Dividing voltage by current gives resistance, $$\mathrm{R}_\mathrm{tot} = \sum_n{R_n}$$.

In the parallel case, $$\mathrm{I_\mathrm{tot}} = \sum_n{I_n}$$ and $$\mathrm{E_\mathrm{tot}}=\mathrm{E}_n$$ for all n. Since $$\mathrm{R}_\mathrm{tot}= {\mathrm{E_\mathrm{tot}} \over \mathrm{I_\mathrm{tot}}} = {\mathrm{E} \over {\sum_n{\mathrm{E} \over{\mathrm{R}_n}}}} = {1 \over {\sum_n{1 \over \mathrm{R_\mathrm{n}}}}}$$

Voltage Drops
A voltage drop is the voltage across a component. In the example of the two resistors in series above, the voltage drop across $$\mathrm{R_1}$$ is $$\mathrm{E_1}.$$ By changing the value of a resistor, the voltage drop across it can be changed, allowing a variable voltage to be created from a fixed voltage.

Power
Resistors restrict the flow of electricity. However, the energy expended doing so must go somewhere. In the case of resistors, the energy is radiated as heat. This is what heats up the filament in a light bulb or the heating elements in a toaster. There is a limit to how much power a resistor can dissipate safely. As a rule, the bigger (in size) the resistor, the more power it can dissipate.

Power is measured in Watts (abbreviated W), with one Watt equal to one Joule per second. In electronics, $$\mathrm{P} = \mathrm{EI}.$$ This permits calculation of the power dissipated by a resistor.


 * 1) If voltage and current are known, then the power is simply their product.
 * 2) If voltage and resistance is known, then:
 * $$\mathrm{P} = \mathrm{EI} = \mathrm{E} \times \frac{\mathrm{E}}{\mathrm{R}} = \frac{\mathrm{E^2}}{\mathrm{R}}.$$
 * 1) If current and resistance are known, then:
 * $$\mathrm{P} = \mathrm{EI} = \mathrm{IR} \times \mathrm{I} = \mathrm{{I^2}R}.$$