Resistance and Resistors

Summary

Introduction

Resistors are electronic components that restrict the flow of current. Figure 1. shows the different resistor symbols that are used in circuit diagrams. The first a rectangular box is used throughout Europe, while the zig-zag line is more common in Japan and the USA.

Figure 1. Resistor symbols in common use.

The unit of resistance is [V.A^-1], which is given the name, the Ohm. [Ω] in honour of the physicist and mathematician, Georg Simon Ohm (1787-1854). Ohm is most famous for the law that bares his name Ohm's law

Inside a Resistor

Resistors are made in several different ways, and although they just look like blobs on a wire, they are quite interesting.

Resistor Networks

Amlost any non-trival electrical circuit will contain some resistors in series and parallel, therefore it is necessary to be able to work out the equivalent resistances of the network.

Series

Resistors in series have the same current flowing across them but different voltages. The total potential drop across the resistors in series is V=V₁ + V₂.

Using Ohm's law

V=IR_eq = IR₁ + IR₂.

R_eq=R₁ + R₂.

The resistance of N different resistors in series is the sum of each resistor.

Parallel

Resistors in parallel share the same voltage but have different currents flowing through them. The total current between the resistors is I_eq=I₁ + I₂.

This is then V/R_eq=V/R₁ + V/R₂.

1/R_eq = I/V= I₁/V₁ + I₂/V₂

1/R_eq= 1/R₁ + 1/R₂

In gereral, the combined resistance of N resistors connected in parallel is 1/R_eq = ∑_i^N(1/R_i)

Temperature Dependence of Resistance

Resistance occurs because electrons flowing through a material

Resistor Colour Coding

Black Brown Red Orange Yellow Green Blue Violet Gray White Black Brown Red Orange Yellow Green Blue Violet Gray White Black Brown Red Orange Yellow Green Blue Violet Gray White Gold Silver Gold Silver None

Javascript Resistance Calculator

The values of the resistor are calculated from the colour of the bands. The values of the colours are shown in Table 1. The first band is the tens values. The second band gives the units, the third band is a multiplying factor the factor being 10^{band value}. The fourth band gives the tolerance of the resistor. No band implies a tolerance of ± 20%, a silver band means the resistor has a tolerance of ± 10% and a gold band has the closest tolerance of ± 5%.

Variable Resistors

Variable resistors can change their resistance.