The resistance in a wire.

Introduction

The resistance in a wire is affected by a number of factors. One of these factors is the cross section of a wire. I will be investigating as to how this affects the resistance in a wire. Another factor that I will also be investigating is the length of the wire.

Cross section of the wire

A wire conducting electricity is affected by a number of factors. One of these factors is the Cross section of the wire. The thickness of the wire affects the resistance of the wire. The cross section a wire:

How does is the resistance of a wire affected by the cross section of the wire? In the flow of electricity electrons are free to move at random within the metal (wire). So if the metal consists of ions rather than metals, it is easier to understand how the flow is affected. When a voltage is applied, the electrons move through the wire. This however is not a steady motion because ions are constantly colliding with each other, slowing them down. When they collide they stop, and start again, and this continues. This is what causes the resistance in a wire – the ions colliding with each other. By increasing the cross section of the wire, the applied voltage will affect more electrons, effectively decreasing the resistance.

From the explanation above, we can derive the fact that the area of the cross section is inversely proportional to the resistance of the wire, or:

RESISTANCE = K/AREA OF CROSS SECTION

RESISTANCE 1/AREA OF CROSS SECTION

Length of the wire

A theory along the same line of this applies to the length of the wire. As described above, in a wire, the ions cause resistance by colliding into each other. When the length of a wire is increased, there are many more ions to collide into each other. Therefore, the chance of ions colliding is increased, and the resistance is increased.

When a circuit is increased in length, it is much more of a struggle for electrons to go round, because there are more obstacles, there are many more wire particles (acting like obstacles) to avoid. Electrons in this case cannot increase or decrease speed, but they can collide. They collide with the particles in the wire. Therefore fewer electrons are able to flow than in a shorter length wire. As a result, the ammeter shows a lower current with the same voltage. In a short circuit there are less particles of wire. This means less collisions and a lower resistance.

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The explanation above enables us to draw the conclusion that the resistance of a wire is directly proportional to the length of the wire, therefore:

RESISTANCE OF WIRE LENGTH OF WIRE

RESISTANCE OF WIRE = K x LENGTH OF WIRE

From the conclusions drawn above, we can now derive the following:

RESISTANCE OF WIRE Length of wire Area of cross-section

RESISTANCE OF WIRE = w l/a

(where w=constant & l=length & a=area)

The constant used in the formula above (w) is the resistivety of the wire or conductor. This also concludes that the resistance of a wire is equal to the resistivety if the wire is 1(m) long, and the cross sectional are is 1(m²).

To calculate the resistivety of the wire (w) we can rearrange the formulae we derived above:

R = w l/a

Ra = wl

R a/l = w

w = R a/l

The resistivety of the wire (w) is measured in Ohms – (Ω).

This information was taken from the book ‘Physics’ by Tom Duncan

Ohm’s Law

Ohms Law is an equation that shows the relationship between Voltage, Current and Resistance in a circuit. This is Ohms law:

V = I x R

R = V / I

I = V / R

Where

V = Voltage

I = Current

R = Resistance

I have attempted below to explain how Ohms law works in an electrical circuit.

The current in a circuit is the flow of electrons. Below is a picture of a piece of metal:

All matter is made up of atoms and each atom is made up of a nucleus that has a certain number of protons and neutrons with an equal number of electrons in orbit.

For example, the diagram below shows a copper atom. It has 29 protons and 29 neutrons in its nucleus, and 29 electrons orbiting the nucleus:

The electrons are arranged in orbits called shells.

In the copper atom (material of the wire), the outer shell (Valence Shell) has only one electron. The electron on the valence shell (Valence electron) can break away from the atom, when it gains sufficient energy. It then becomes a free electron.

The energy required for the electron to break away is very easy to provide. The energy can come from heat light or electricity. When the electron becomes free it leaves behind a positive charge. This is because protons are positive, neutrons are neutral and electrons are negative. So when there were 29 electrons, and 29 protons, the charge was neutral. Now there is one less electron, so the positive charge is higher. Now the copper atom is unbalanced, and it will always try to get an electron back into its orbit, in order to balance itself.

Electric current is the movement of electrons from one atom to another in a conductor.

Now it is easier to visualize a piece of copper wire, with billions of atoms, each one of them losing an electron and all the electrons jumping to other atoms. This is what current is.

Current is the movement of electrons in a conductor (in this case copper wire).

The more electrons that move in a conductor the more current you have in the circuit.

The current is measured in Amperes (A), and the symbol is ‘I’.

The resistance in a circuit is the opposition of electron flow and is based on the physical size of the conductors. The current is the movement of free electrons in a circuit therefore, the number of atoms in a wire make a big difference as to how many electrons can flow at any given time. As explained above (cross section of a wire); “The bigger the diameter a wire is, the more ions there are in the wire, so the more free electrons”. The opposite of this is resistance: “The smaller the diameter of wire the fewer the number of ions so the fewer the number of free electrons, i.e. less current”.

A small (carbon) resist or

A smaller wire can be used to control the amount of current flowing in a circuit, because it allows less current to travel through it. The name we give to this opposition is called RESISTANCE and the symbol is R. The resistance is measured in OHMS (Ω).

Resistors are components that are manufactured to have a specific amount of resistance and are marked with various values of OHMS. The markings on a common resistor are in the form of colored bands around the resistor body. To read the value of a resistor you must know the color code used for the number system. Below is a picture of a resistor with its colored bands labeled.

(This picture was taken from )

The voltage is the potential difference in a circuit. It is caused by the unbalanced state of atoms. As shown above with the copper atom, when an electron leaves the orbit of an atom it leaves a positive charge. In order to re-stabilize itself, the (now positive) atom will attract any (negative) electron, so that it can go back into a normal state. To have flow in a current, there must be atoms present with missing electrons, and a source of negative electrons.

“If these sources of charges have a current path to flow through then the electrons will be attracted to the positive atoms to fill the holes. You need a complete circuit made of conductive material in order to have current flow and the current will flow from the negative source to the positive source.” - (http://www.technology.niagarac.on.ca/students/cmukendi/what_is_current.html)

Below is a battery shown as a voltage source. The top half is all positive charges and the bottom half all negative:

This is how the battery can be used as a source to produce current:

Ohms law states that if you have one volt applied to a one ohm resistance the current will be one amp.

Knowing that, it is possible to calculate the voltage, resistance and current in a circuit if you know 2 of the values using the equations V=IxR, R=V/I and I=V/R

This is why Ohms law makes sense and is correct.

From all information I have presented in my introduction, it is now fair to conclude that:

RESISTANCE = K/AREA OF CROSS SECTION (k = constant)

RESISTANCE = K x LENGTH OF WIRE