Describe how you would investigate the properties of a piece of wire so as to enable an electrician to make a resistor of the required value.

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Physics Coursework

The Problem

In catalogues such as R.S components, Malpin, Cpc etc resistors are listed with certain fixed values, e.g.) 47Ώ.

While repairing an old piece of electrical/electronic equipment an electrician discovered that he needed to replace a resistor with a value not listed in any of the catalogues. Describe how you would investigate the properties of a piece of wire so as to enable him to make a resistor of the required value.

Background Knowledge.

To carry out an investigation dealing with resistance and electricity, we firstly need to know about what resistance is. The resistance is the opposition of a conductor to current. It occurs when electrons travelling along the wire collide with the ions in the wire. It could also be described as a measure of how hard it is to move the electrons/ions through a wire.

The current is the rate of the flow of charge and the voltage is the energy transferred per unit charge.

To measure the resistance you need to know the current flowing through a circuit and also the voltage. These can be measured by using an ammeter for current and a voltmeter for voltage.

The relationship between voltage, current and resistance is known as Ohms law. Resistance is measured in Ohms.

Ohms law states that the current through a metallic conductor is directly proportional to the voltage across it providing its temperature and physical conditions remain the same.

The equation connecting resistance to voltage and current is V=IR, where V is voltage, I is current and R is resistance. Conductors intended to have resistance is just the sum of all the resistances.

In a parallel circuit the total resistance is always less than the branch with the smallest resistance. The equation for this is R=R1+R2+R3.

Another equation which is also useful is the equation for Resistivity. This is:

Resistance also depends on temperature, because if the wire is heated up the ions in the wire will start to vibrate because of their energy increase. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.

In planning for this experiment I came across yet another equation which may be useful. This is the equation for Drift Velocity:

I=nAeV

Where:

n= number of electrons per m3

A=cross sectional area

E=charge on the electron (-1.6×10-19)

V=drift velocity.

I also know that as the drift velocity decreases the current decreases and so the resistance decreases. This happens with a longer wire.

Variables.

The factors that are likely to affect the resistance of a wire are:

The length of the wire

The cross sectional area

The temperature of the wire

The alloy/type/Resistivity of the wire

The length of the wire could affect the resistance because the longer the piece of wire the longer the electrons have to travel, therefore more resistance and also the fact that there are more collisions so it is slowed down.

Due to this the length increase should be proportional to the resistance increase.

If the cross sectional area of the wire is increased the resistance will decrease this is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be fewer collisions.

Temperature could affect the resistance. This is because the heat gives the particles more energy to vibrate and move so this delays the time taken for the electrons to reach the end of the wire.

The type of material will affect the amount of free electrons which are able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the electrons, so if there are more or larger atoms then there will be a high number of electrons causing a lower resistance because of the increase in the number of electrons. The resistance will also increase if the atoms of a material are more closely packed.

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In my investigation I am going to look at two different variables- the length of a wire and the cross sectional area of a wire.

Firstly I am going to investigate the length I will measure and record the resistance, it will be the dependant variable. The independent variable will be the length and the temperature, material and cross sectional are will all be controlled variables. To control the temperature of the wire we will use a long piece of wire so it doesn’t overheat and affect the resistance, and we will also remove the key in the ...

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