Resistivity


Aim: To investigate the physical and electrical properties of a wire in order to find the resistance using Ohmís law and from this to find the Resistivity of the wire at room temperature.


Hypothesis:


Electricity is the flow of charged particles around a complete circuit; a circuit consists of three main factors, voltage, current and resistance.


Ohmís Law states that at a constant room temperature these factors can be related by the equation,


V = IR


Where, V = Voltage (V)


I = Current (A)


R = Resistance (Ώ)


Therefore, we can say that at a constant room temperature resistance is relative to the value of the voltage and of the current, this can be expressed by the equation,





By altering the values of voltage and current the value of resistance can be altered at any given point in a circuit. In addition to the relationship stated in Ohmís Law, resistance is related to length and cross sectional area.


By saying that resistance is due to collisions between electrons we can deduce that resistance is proportional to length because by doubling the length of a wire we double the chance of a charged particle colliding (resistance), therefore,


R ∞ L


Also, if we double the area it will consequently double the number of charged particles flowing at a given point and thus double the current and halving the resistance. Therefore,





By combining these equations we can produce,





Where, = Resistivity (Ώ/m) (material constant)


R = Resistance (Ώ)


a = Cross Sectional Area (mm≤)


L = Length (m)


Resistivity is a constant of a wire, it is the resistance of a standard size wire of a material with 1 unit length and 1 unit cross sectional area, so 1m long with a cross sectional area of 1m≤.


I intend to investigate the constancy of resistivity; if resistivity is indeed a constant then it will be the same at every point along a chosen wire.


The standard deviation of the results can be calculated by using this equation,





By using the standard deviation of the results I predict that at every point tested along the chosen wire the resistivity will be within 2 standard deviations of the mean resistivity of the wire.


Approximately 97% of a sample will lie within 2 standard deviations of the mean, and approximately 99% of a sample lie within 3 standard deviations of the mean. Providing that all the results lie within 2 standard deviations of the mean, then it can be taken that resistivity is a constant.


Experimental Variables


The variables identified in this experiment are as follows,


Voltage


Current


Resistance


Length


Cross Sectional Area


Temperature


Throughout the experiment it will be assumed that there are no other variables present, and that temperature is constant at room temperature.


All the variables will be kept as close to constant as possible, barring length which will be the experimental variable and thus will be altered.


Experimental Procedure Theory


In order to calculate resistivity the voltage and current will be taken at a designated point along a wire, these values will then be used to calculate resistance using Ohmís Law as shown,





This can then be combined with,





This will produce the equation,





The values used will be recorded and then this process repeated at a decided interval along a 1m length of wire.


Prior to this, the wire to use and the interval regularity must first be deiced, and safety precautions taken into account.


Preliminary Experiment


An array of wires were made available that varied in type and SWG (Standard Wire Gauge) values.


Copper SWG 30


Constanton SWG 28


SWG 30


Nickel Chrome SWG 18


SWG 22


SWG 30


In order to determine the appropriate wire for experimentation, a preliminary experiment was performed testing each wires resistive properties at 50cm length and 100cm length while using a power supply stated as being 6V with a supplied current of 1A.


The results were as follows,


Material


SWG


Length (cm)


PD (V)


Curent (A)


Resistance (Ώ)


Copper


30


50


0.30


1.08


0.28


100


0.35


1.09


0.32


Constanton


28


50


2.55


1.06


2.40


100


4.55


0.93


4.89


30


50


3.30


1.03


3.20


100


5.10


0.83


6.10


Nickel Chrome


18


50


0.62


1.09


0.57


100


1.16


1.09


1.06


28


50


1.80


1.07


1.68


100


3.00


1.04


2.88


30


50


5.43


0.72


7.54


100


5.95


0.41


14.51


Theses results were then used to determine which wire would be most appropriate for use in the experiment.


Preliminary Conclusion


It was decided from the data supplied by the preliminary experiment that the most suitable wire for use in this investigation would be Constanton with an SWG value of 30.


At 50cm the resistance was calculated as being 3.20Ώ and at 100cm the resistance was calculated as being 6.10Ώ this demonstrates an almost 100% increase in resistance over the length of 100cm,