Required practical: measuring the resistivity of a wire

Aim

• Determine the resistivityA material property that quantifies how strongly it resists currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohm-metres (Ω m). of a constantan wire by measuring how resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω). varies with length.

Variables

• Independent variable: length L of the wire.
• Dependent variable: current I through the wire (used to calculate R).
• Control variables: voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. across the wire, material of the wire, temperature of the wire.

Method

• Measure the diameter of the constantan wire using a micrometerA precision measuring instrument used to measure small distances or thicknesses, typically to the nearest 0.01 mm. at 5 to 10 points along its length.
• Calculate the mean diameter, then the cross-sectional area: $A = \pi d^{2}/4$.
• Tape or clamp the wire to a metre ruler. Connect one end to the circuit at the 0 mark.
• Use a flying lead with a crocodile clip to make contact at measured lengths along the wire.
• Connect an ammeterAn instrument that measures current. Connected in series with the component. Has very low resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). so it doesn't affect the circuit. in series and a voltmeterAn instrument that measures potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V).. Connected in parallel across the component. Has very high resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω).. in parallel with the wire.
• Set the powerThe rate of energy transfer. Measured in watts (W). supply to a fixed voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. (e.g. 6.0 V). Check with the voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance..
• Record the current at each length. Switch off immediately after each reading to prevent heating.
• Vary the length in equal intervals (e.g. 0.25 m steps from 0.25 m to 2.00 m) for 8 to 10 readings.
• Repeat each current measurement at least 3 times and calculate a mean.

Analysis

• Calculate resistance for each length: $R = V / I$.
• Plot R (y-axis) against L (x-axis).
• The equation $R = \rho L / A has$ the form $y = mx$, so the graph is a straight line through the origin.
• $Gradient = \\rho /\;\text{A}.$
• ResistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m).: $\rho = gradient \times A$.

Evaluation

• Systematic errorAn error that shifts all readings by the same amount in the same direction. Cannot be reduced by repeating measurements.: if the wire does not start at 0 on the ruler, all lengths have a zero error. Ensure the fixed end aligns with the 0 mark.
• Random errorAn error that causes readings to scatter unpredictably above and below the true value. Can be reduced by averaging repeated measurements.: the wire heats up when current flows, changing its resistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m).. Keep currents small and switch off between readings.
• Random errorAn error that causes readings to scatter unpredictably above and below the true value. Can be reduced by averaging repeated measurements.: the diameter may not be uniform. Take 5 to 10 readings at different points and use the mean.
• ResolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm.: micrometer = 0.01 mm, metre ruler = 1 mm, ammeterAn instrument that measures current. Connected in series with the component. Has very low resistance so it doesn't affect the circuit. = 0.01 A, $voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. = 0.1 V$.

Safety

• Thin wire carrying high current gets very hot. Do not touch the wire when the circuit is on.
• Switch off immediately if you smell burning.
• Keep liquids away from electrical equipment.