The aim of the investigation is to determine the resistivity of nichrome wire at varying dimensions. The nichrome wire is of 1 metre at 32 gauge and also of 0. 5 metre at 28 gauge. Resistivity is an electrical measure indicating how strongly a material opposes the flow of electric current. A low resistivity indicates the material readily allows the movement of electrical charge.
The standard imperial unit of electrical resistivity is the ohm metre (? m). The electrical resistivity ? (rho) of a material is measured as its resistance to current per metre length for a uniform cross section and is usually defined by the following: Where:? is the resistivity (? m) R is the electrical resistance (? ) l is the length of the wire (metre).
A is the cross-sectional area of the wire (square metres) Nichrome is a nickel-chromium alloy commonly used in heating elements. The typical resistivity of nichrome at 293 K is 1. 50 i?? 10-6 ? m. Hypothesis The three factors that affect the resistance of a wire would be the thickness, length and the material type. Between a thin wire and a thick wire, the latter will have less resistance as there is more area for the electrons to pass through. The length of the wire affects the resistance as of the distance the current must travel.
A longer wire would have more resistance then that which is shorter. Thus, the prediction here is that although there will be different resistances between two wires of different dimensions, the overall resistivity calculated for nichrome will be the same, as it is calculated per metre for a uniform cross-sectional area. Equipment 0. 5 m (32 gauge) Nichrome wire 1 m (28 gauge) Nichrome wire Voltmeter Ammeter Power supply/ Battery pack 5 Wires 2 Crocodile clips Terminal block Diagram Procedure The equipment was set up as shown above. The first nichrome wire was measured using the metre ruler and cut.
The dimensions were 32 gauge and length of 1 metre. It was attached to the apparatus. The power supply was set to 2 volts and the current and voltage was measured using the voltmeter and ammeter respectively. Readings were recorded in the results table. This was repeated at different volt settings, 4 – 16 volts. The whole procedure was once again repeated for another nichrome wire of different dimensions, being at 28 gauge and of 0. 5 metre. Results Table 1: the resistivity of nichrome wire at 32 gauge and 1 metre length. Power Voltage (V) Current (A) Resistance (? ) Resistivity (? m)
Table 2: the resistivity of nichrome wire at 28 gauge and 0. 5 metre length Power Voltage (V) Current (A) Resistance (? ) Resistivity (? m) 1. 1477E-06 Mean 4. 9300 1. 0948E-06 Sample Calculations Resistance (? ) The resistance was measured using the currents and voltages measured during the experiment. The formula for resistance is:
Resistivity (? m) The electrical resistivity of an element is the measure indicating how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electrical charge. ? = resistivity R = resistance A = cross-sectional area.
Resistivity as calculated from the graph: ?or the 28 gauge Uncertainty The Heisenberg uncertainty principle states that one cannot assign, with full precision, values for certain pairs of observable variables. This would also apply to this investigation where we have uncertainties to the readings taken. All readings would have these uncertainties above and below the reading. To find the percentage uncertainty we apply the following formula.
% uncertainty = uncertainty x 100 reading taken The uncertainties of the apparatus are shown below. This can play a major role in any errors or anomalies found. Metre Ruler ?? 0. 0005m Voltmeter ?? 0. 01volts Ammeter ?? 0. 01amps Metre Ruler The ruler was used to measure the length of the wire. The end of the wire was held at zero centimetres and the other end was measured and cut. % uncertainty =?? 0. 0005 x 100 1 = ?? 0. 1 % Length (m) % uncertainty (1 Voltmeter The voltmeter was used to measure the voltage of the wire connected to this circuit.