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Factors Affecting the Resistance of a wire.

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Introduction

FACTORS AFFECTING THE RESISTANCE OF A WIRE

BY FAHAD ASHRAF

BACKGROUND KNOWLEDGE

An electric current (I) is a flow of charge. In an electric conductor, the charge is carried by ‘conduction’ electrons, which are not attached to fixed atoms in the conductor. The conduction electrons move randomly at high speeds such that there is no net current. When a potential difference (V) is applied across the conductor, the free electrons are made to drift towards the positive terminal, thus giving a flow of charge across the conductor. The relationship between the potential difference, V, and the resulting current, I, known as ohm’s law is:

V= IR

Where R is the resistance.

Resistance is the impedance to the flow of current and is measured in ohms (Ω). It is a result of atoms in the conductor vibrating and interfering with the drift of the electrons.  When a power supply is connected across a conductor, it causes the electrons to accelerate from the negative terminal to the positive terminal. The electrons collide with the vibrating atoms and move off in a random direction and are then accelerated again by the power supply.  The electrons are continuously gaining energy from the supply and transferring it to the conductor’s atoms when they collide. The atoms gain energy and the conductor gets hotter (resistive heating).

Electrons being accelerated along the wire and colliding with fixed atoms

Investigations show that the resistance of a uniform conductor depends on:

  • Length (l)

...read more.

Middle

Aim: To investigate the effect of length on the resistance of a conducting wire.

The length of a conducting wire will be varied, and the resistance determined by measuring the potential difference and the current and then using ohms law. The following variables will be kept constant in order to ensure a fair test: temperature, cross sectional area and type of wire.

Prediction: If the length of the wire is doubled, the resistance of the wire will also double (i.e. the resistance is directly proportional to the length).  This is because as the length of a conductor is increased, there are more collisions between the conduction electrons and the conductor’s atoms. Therefore it is more difficult for electrons to go all the way through the conductor and hence the resistance is larger. If the conductor is twice as large there will be twice as many collisions and hence the resistance of the conductor will be doubled. A graph of resistance versus length should look like:

image01.png

METHOD

List of Apparatus:

  • Copper wire (0.9mm thickness)
  • Amp meter
  • Voltmeter
  • Power supply
  • Meter rule
  • Crocodile clips

The following circuit was setup to determine the resistance of the varying lengths of wire:

  1. The experiment was setup as shown in the diagram above. The ammeter is connected in series and the voltmeter in parallel.
  2. The crocodile clip was placed at the 25 cm mark, and the reading on the voltmeter and ammeter was noted.
...read more.

Conclusion

The errors in the experiment where due to the resistive heating of the wire and the fluctuations in the output of the ammeter and voltmeter.  Resistive heating increases the resistance of the wire, and this can happen very quickly if a large current flows. The error due to heating was minimised by taking the V-I readings as quickly as possible, before the wire had time to heat up significantly. Also we allowed time in between taking measurements for the wire to cool down. To reduce the error due to the fluctuations in the ammeter and voltmeter, we tried to determine the mean value of the fluctuating reading. Also we repeated the experiment three times in order to reduce any random errors due the fluctuations and any other human errors.

The experiment could be extended by investigating whether the relationship between length and resistance is maintained when wires of different materials and different cross sections are used. It could be further extended by investigating other variables, which affect the resistance of a wire (i.e. cross sectional area, type of material and temperature).  

Fahad Ashraf

...read more.

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