What it shows
A Wheatstone bridge is balanced when the galvanometer shows zero, and then the unknown resistance equals the known one multiplied by the ratio of the two wire lengths (X = R l / (100 minus l)). A home-built metre bridge measures resistors to within a few percent.
The science
In a Wheatstone bridge four resistances form a loop with a cell across one diagonal and a galvanometer across the other; when R1/R2 = R3/R4 the two middle points sit at the same potential and no current flows through the galvanometer. In the metre bridge two of the arms are the two parts of a uniform wire whose resistances are proportional to their lengths l and 100 minus l. So at balance X / R = l / (100 minus l). Because the measurement depends only on a null reading and a length ratio, the result does not depend on the cell voltage or the galvanometer calibration, which makes the method very accurate.
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.
- A 1 m length of 28 SWG nichrome or constantan wire
- A 1.1 m wooden plank with a paper metre scale glued on
- Three brass or copper strips with screw terminals (an electrician can supply strips), or large crocodile clips
- A centre-zero galvanometer from the lab, or a multimeter on its lowest DC millivolt range
- Two AA cells, a switch and a jockey (a sharpened wire on a wooden handle)
- Known resistors: 10, 22, 47 and 100 ohm and one unmarked resistor
Safety
For this project: Cells only. Press the jockey briefly rather than sliding it, so the wire is not scraped thin. An adult must fix the terminal strips with screws.
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.
All the safety rulesStep by step
9 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.
Stretch the wire tight along the scale from the 0 to the 100 cm mark and clamp both ends under the two outer metal strips.
Fix the third strip in the middle, leaving two gaps: the left gap for the unknown X and the right gap for the known R.
Connect the cells and switch across the two ends of the wire, and the galvanometer between the middle strip and the jockey.
Put the unknown resistor in the left gap and the 47 ohm resistor in the right gap, close the switch, and press the jockey near 50 cm.
Move the jockey left or right until the galvanometer reads exactly zero and record the balance length l.
Swap X and R between the gaps and find the new balance length; average the two values of X to cancel end errors.
Repeat with 22 and 100 ohm as the known resistor and record a table of R, l, 100 minus l, and the calculated X.
Check X with the multimeter on ohms and compare; then use the bridge to confirm the series and parallel formulas with two known resistors.
Explain in your report why the balance point should be kept between 30 and 70 cm for best accuracy.
What you should see
A balance point with zero galvanometer deflection, and a calculated unknown resistance within about 3 percent of the multimeter value, with the series and parallel combinations also matching the formulas.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the balance condition of a Wheatstone bridge?
The ratio of resistances in the two arms is equal, so no current flows through the galvanometer.
2Why is the result independent of the cell voltage?
The balance is a null point; only the ratio of lengths matters, not how much current flows.
3Why use a thick copper strip rather than a wire for the connections?
To keep the resistance of the connections negligible compared with the arms.
4Why keep the balance point near the middle?
A small error in reading l then gives the smallest percentage error in the ratio.
Take it further
Measure the resistance of a coil of wire at room temperature and in hot water to find its temperature coefficient of resistance.
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.
Free ebooks for this project
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