What it shows
The resistance of a wire is directly proportional to its length and inversely proportional to its area of cross section (R = rho L / A). Doubling the length doubles R, and joining two equal wires side by side in parallel halves it.
The science
Electrons moving through a wire collide with the ions of the metal. A longer wire gives more collisions along the path, so more resistance; a thicker wire gives more parallel paths, so less resistance. Nichrome has a high resistivity (about 1.1 x 10^-6 ohm metre) so even 20 cm of thin wire shows a resistance of a few ohms that a multimeter can read, which a copper wire of the same length would not (its resistance would be only a few hundredths of an ohm). Measuring R for 20, 40, 60, 80 and 100 cm gives a straight line through the origin when R is plotted against L.
Materials
Cost: under Rs 500. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- About 2 m of thin nichrome heater wire, 30 to 32 SWG (from an electrical repair shop, under Rs 40), or eureka (constantan) wire of similar thickness
- A metre scale and a wooden plank to tape the wire along
- Two AA cells in a holder
- A 22 ohm resistor to limit the current in the cell test
- A digital multimeter
- Crocodile clip leads
- A screw gauge from the lab, or the wire gauge printed on the packet
Safety
For this project: Measure resistance with the meter on its ohm range first, which uses no cells. In the cell test keep the 22 ohm resistor in the loop, because nichrome gets warm when current flows; keep the circuit closed only while reading. Cut wire with pliers, not a knife, and an adult must help with the cut ends, which are sharp.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Tape the nichrome wire straight along the metre scale on the plank, with one crocodile clip fixed at the zero mark.
Set the multimeter to its lowest ohm range and touch the probes together to note the lead resistance. Then connect the meter across the fixed clip and a second clip placed on the wire at 20 cm, and record the resistance minus the lead resistance.
Move the second clip to 40, 60, 80 and 100 cm and record each resistance in a table with columns for length, R, and R/L.
Check with cells: connect two cells, the 22 ohm resistor, the wire length and the meter on milliamps in series, and show that the current falls as the length grows.
Plot R against L on graph paper; the points should lie close to a straight line through the origin.
Lay two equal 50 cm lengths side by side without touching, join their ends with clips so they are in parallel, measure the combined resistance, and compare with a single 50 cm length.
Measure the diameter with a screw gauge, compute the area A = pi d^2 / 4, and work out the resistivity rho = R A / L from your slope.
Compare your resistivity with the textbook value for nichrome and list the reasons for any difference in your report.
What you should see
A straight-line R-L graph, a double wire in parallel showing about half the resistance of a single one, and a calculated resistivity within about 30 percent of the accepted value for nichrome.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01State the relation between resistance, length and area.
R = rho L / A, where rho is the resistivity of the material.
02Why use nichrome rather than copper?
Nichrome has a much higher resistivity, so short lengths give resistances large enough to measure.
03What is the SI unit of resistivity?
Ohm metre.
04Why does joining two equal wires side by side halve the resistance?
They act as two equal resistors in parallel, which gives half the resistance of one.
Take it further
Repeat with wires of two different gauges and plot R against 1/A for a fixed length.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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