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# Investigate one or more factors affecting the resistance of metal wires

Extracts from this document...

Introduction

Aim: To investigate one or more factors that affects the resistance of metal wires

Plan

Resistance is the force that opposes the flow of charge i.e. an electrical current around a circuit. This means that energy is required to push the charged particles around the circuit. Resistance involves collisions between the electrons in the wire and the atoms (strictly speaking ions) that make up the structure of the conductor. As we have already encountered, the higher the resistance, the lower the current. If there is a high resistance, to get the same current, a higher voltage will be needed to provide an extra push for the electricity to flow.

Resistance is measured in units called Ohms, symbol Ω. A conductor has a resistance of one ohm (1.0 Ω) if there is a current of one ampere (1.0A) through it when the voltage (potential difference) across it is one volt (1.0V). In order to calculate the resistance, you must know the voltage and the current.

## Mechanism of conduction of electricity in metals

Metals are made up of a lattice of ions (charged particles). The structure of metals is such that each of its atoms (on average) has one outer electron, which is not needed for bonding, and which does not need to remain restricted on its atom leaving a positive ion. As these “free” electrons “drift” through the crystal lattice, when a potential difference is applied, they collide with the positive ions of the lattice. These collisions slow down the flow of electrons (electric current). During the collision, the kinetic energy, which an electron has gained due to acceleration, is transferred to the ion with which it has collided. This transfer on collision is the cause of resistance. In turn, the crystal lattice gains kinetic energy, which produces a rise in temperature of the conductor.

Middle

There are two ways in which we could measure the resistance of a wire. The first one is to use an ohmmeter. Ohmmeters are useful in the sense that they provide a quick and direct readout. However, I have discovered that it would be more accurate for me to work out the resistance of the wire using the formula:

Resistance = Voltage/Current or R=V/I

since you do not have to worry about the resistance of the connecting wires.

In order to be able to find the resistance using this formula, I must measure the potential difference across the wire being investigated (in Volts) and the current through the wire (in Amps).

Number of measurements

Resistance and Length

The length of the Constantan wire between the crocodile clips will be varied from 10 cm to 100 cm and I will take ammeter readings in 10 cm intervals i.e. 10 cm, 20 cm, 30 cm etc. This will give a total of 10 pairs of values (since I will repeat the whole experiment once), which is a good range or results and an adequate number of measurements to allow me to draw the predicted straight-line graph.

Resistance and Area

In order to investigate the cross-sectional area, I had decided that I would take ammeter readings at 10cm intervals of a length of 1m wire. I would investigate the effect of cross-sectional area by comparing the different thicknesses of the wires at particular lengths.

I would work out the cross-sectional area of the wire (in m²) using the formula:

A = π x (radius) ²

=  π x (diameter/2) ²

or, in m², A = πd² /4

Diagram:

1. The circuit was set up as in the diagram above.
2. I marked out the length of the wire between 10cm and 100cm in steps of 10cm, i.e. 10cm, 20cm etc on the wooden board using a meter ruler.

Conclusion

I could have done more tests around any anomalous points that I found to ensure the accuracy of my experiment. I should have done my experiments at 1.5V as well as 3V and 4.5V because I assume that the results at 1.5V will be much more accurate since a lower current would be applied. Where a lower current is applied, you need to measure to 3 decimal places – it is therefore necessary to use an ammeter.  I would add a fixed resistance in the circuit as well as the length of the wire, which would ensure that my readings are accurate.

One suggestion made from a source of reference to improve the experiment would be to place the wire in a water bath to let the heat flow out and keep the temperature constant (i.e. the temperature of the wire would have been the same as the water bath). I would not do this because it is dangerous to allow electricity to come in contact with water.

Future experiments

• To improve upon the results that I have already made, the next stage in this experiment would be to measure the potential difference across the wire rather than have relayed on the battery pack maintaining a fixed voltage as the current changed.
• I would use different types of resistance wire (e.g. manganin) to compare them to constantan – if I were to do this, it would be very important to keep the temperature constant for example by using a variable resistor.
• I would take more readings for different diameters of wire at the same length and at a constant voltage supply. This would then allow me to plot a graph and come to an accurate conclusion.

In the future, I would also like to compare my figure of length with the theoretical resistivity of constantan to validate my readings. Through research, I have come to know that the resistivity of Constantan is: 5.0 x 10-7 Ohmic metres.

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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