# The length of the wire - Sample Essay

An Investigation into the Factors Affecting the Resistance of a Wire Safety The normal safety rules regarding the use of Mains Electricity apply. The wire used to make the resistor can get very hot during the experiment. It is important to remember this and not touch the wire while the power supply is switched on or soon after the power supply is switched off. The normal laboratory safety rules apply. Variables o The potential difference across the wire. o The electric current through the wire These two variables will be used to calculate the resistance of the wire. o The length of the wire.

o The cross-sectional area of the wire. All other factors will be kept constant during the investigation. o The material from which the wire is made. o The temperature of the wire. This will be difficult to arrange and so Constantan wire will be used. The resistivity of Constantan wire does not vary greatly with temperature. Scientific Background I have found out the following information by reading about the subject. The resistance of a resistor can be calculated from the relationship Resistance = Voltage Current R = V I where R is Resistance measured in Ohms (? ) V is Voltage measured in Volts (V).

I is Electric Current measured in Amps (A) The longer the length of the wire, the greater its resistance, because the longer the wire, the further the electrons have to travel. Resistance (R) is directly proportional to the length of the wire (L) as long as the cross-sectional area is constant. R ?? L The greater the cross-sectional area (A) of the wire (conductor), the lower its resistance, because the electrons have more ways in which they can travel through the wire. Resistance (R) is inversely proportional to the cross-sectional area of the wire (A) as long as the length of the wire is constant.

R ? 1/A The resistance of a wire also depends upon the material that it is made from. This will not be a subject studied in this investigation. The resistance of a metal wire also depends upon its temperature. The temperature of the wire will vary but the resistance of the material used, Constantan, does not vary greatly with temperature Combining the Proportionalities The two proportionalities R ?? L and R ? 1/A can be combined to give R ? L/A This can be turned into an equality by multiplying one side by a constant R ??? L/A where ? is a constant for the material called resistivity.

R is the resistance of the wire measured in Ohms. L is the length of the wire measured in metres A is the cross-sectional area measured in metres squared. ? is the Resistivity of the wire measured in Ohm-metres. An Explanation Resistance and Length If we consider a length of wire as a resistor, say 0. 1m, then it will have a certain value for its resistance, say R. A 0. 2m length of wire can be thought of as two of these resistors in series.

Since resistors in series just add up, the total resistance of this combination is 2R. The same thinking can be applied to a 0.3m length which will have a total resistance of 3R. Doubling the length of the wire, doubles the resistance. Trebling the length of the wire trebles the resistance etc. The Resistance of the wire is directly proportional to its length. R ?? L Resistance and Cross-Sectional Area We can change the cross-sectional area of the wire by connecting two identical pieces of wire side by side. With two pieces of wire side by side the electric current has twice as many ways to go, the resistance of the combination will be halved. The cross-sectional area has doubled and the resistance will be half that of one wire on its own.

With three pieces of wire side by side the electric current has three times as many ways to go, the resistance of the combination will be one third. The cross-sectional area has trebled and the resistance will be one third that of one wire on its own. The Resistance of the wire is inversely proportional to its cross-sectional area. R ? 1/A Measuring Resistance Resistance = Potential Difference Current In order to measure the resistance of a wire or a combination of wires we have to measure the potential difference across the resistor in Volts and the Current through the resistor in Amps.