An Investigation Into Electrical Resistance

An Investigation Into Electrical Resistance
Resistance, in electricity, is a property of any object or substance to resist the flow of an electrical current. The quantity of resistance in an electric circuit determines the amount of current flowing in the circuit for any given voltage applied to the circuit. The resistance of an object is determined by the nature of the substance of which it is composed, its resistivity, accounting for its dimensions and its temperature. Resistivity is expressed in terms of Ohms / cm3 at 20ºC. An electrical conductor is any material that offers little resistance to the flow of an electric current. The difference between a conductor and an insulator, which is a poor conductor of electricity, is one of degree rather than kind, because all substances conduct electricity to some extent. A good conductor of electricity, such as silver or copper, may have a conductivity billions of times as great, or more, as the conductivity of a good insulator, such as glass or mica.Method

We were set the task of investigating the factors that come into play when determining the resistance of a piece of wire. We would be provided with the necessary apparatus needed to carry out the investigations. The basic setup would involve a circuit with a set of cells connected in series with an ammeter and the piece of wire being investigated, and a voltmeter connected in parallel with the wire. The ammeter is placed in series with the wire. An ammeter has a low resistance, so that it introduces as little extra resistance as possible into the circuit. The voltmeter is connected in parallel with the wire. Voltmeters have a high resistance, so the current they take is usually negligible.

We decided on the variables that could affect the resistance of a wire:

 Length of the wire

 Thickness of the wire

 The material used as the wire

 Temperature

We were to investigate as many of these factors as possible given a limited period of time. We would carry out a set of experiments where in each one we changed one variable while keeping the others constant. In each case we would have to measure the current passing through the circuit and the potential difference across the wire; given these the resistance could be calculated using the formula R=v/i, where R is the resistance in Ohms, v is the potential difference in Volts, and i is the current in Amperes. This formula basically states that 1 V will cause a current of 1 A to pass through a resistance of 1 Ohm. In an electric circuit electrons pass through the wires. Metals, having a giant structure as a characteristic, contain free electrons in their atoms which can move almost unhindered through the metal when a potential difference is applied. Resistance is caused by obstructions in the pathways of the electrons: these obstructions are basically the nuclei of the metal atoms. The heat that is caused in resistance wires is attributable to this factor: the inelastic collisions between the electrons and nuclei causes kinetic energy to be changed into heat energy.

Length of the wire

If a wire of certain length has a resistance R then a wire twice its length should have a resistance 2R. This is because having a wire twice the length is the same as having two wires of the initial length placed in series, and the formula for this is Rtotal=R1+R2. R1 and R2 are in this case the same and can be written simply as R, so that Rtotal can be seen to equal 2R. This can be applied to wires half the length of the initial wire (½R), or three times the length (3R), or any other multiple of the initial length (nR).

This can be explained by the movement of electrons through the wire. A wire twice the length of the initial wire has twice the number of metal atom nuclei for the same number of electrons to collide into in the same amount of time. Thus the resistance is doubled.

We have therefore that R is proportional to l where R is resistance and l length of the wire.

Thickness of the Wire

When talking about the thickness of a wire it is better to resort to cross-sectional area of the wire rather than diameter. So a wire that is twice as thick as another wire has double the cross-sectional area of the other wire. Having a wire twice as thick is the same as having two wires of the initial thickness placed in parallel to each other. The equation for this is 1/Rtotal=1/R1+1/R2. R1 and R2 are again the same and can both be written as R. Therefore 1/Rtotal=2/R and Rtotal=R/2. We can see that a wire twice as thick as the initial wire has half the initial resistance. This can again be applied to different multiples of wire thickness.

Using the movement of electrons idea we see that a wire with twice the cross-sectional area has twice the number of electrons travelling across the wires in the same period of time.

Therefore R is proportional to 1/A where R is resistance and A the cross-sectional area of the wire.

The material used as the wire

Different metals have different atomic compositions, both in structure and in size. Differences in structure and nucleus size can change the resistance: electrons may move more freely in atomic structures of one type rather than another (close packing versus body-centred cubic structures, for example); the size of the nuclei may mean that there are more collisions between them and the electrons. There is also the case of alloys, mixtures of two or more metal elements: these can change the resistance properties.

Temperature

Increasing the surrounding temperature means supplying more energy to the particles in the wires. This may have the effect of increasing the resistance as the particles, because of energy gains, reach a higher level of excitement and vibrate with more vigour. This would have the effect of more collisions between the electrons and nuclei and therefore higher resistance.

Wheatstone Bridge, an Alternative Method

There is another method of measuring the resistance of a wire, which involves using a circuit known as a Wheatstone bridge, named after the British physicist Charles Wheatstone. This gives accurate measurements of resistance using a galvanometer. This circuit consists of three known resistances and an unknown resistance connected in a diamond pattern. A DC voltage is connected across two opposite points of the diamond, and a galvanometer is bridged across the other two points. When all four of the resistances bear a fixed relationship to each other, the currents flowing through the two arms of the circuit will be equal, and no current will flow through the galvanometer. By varying the value of one of the known resistances, the bridge can be made to balance for any value of unknown resistance, which can then be calculated from the values of the other resistors.

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