The resistivity ρ of a material is the resistance of a piece of material with unit cross sectional area and unit length. The resistance of a wire is proportional to its length L and inverse proportional to its cross-sectional area A. We have R = ρl/A. The unit of resistivity is Ωm.
The table below gives you ρL for each wire and you can calculate A = πr2. Make sure you use SI units.
| Coil # |
Type |
resistivity (10-8Ωm) |
Length L m |
Radius (10-4m) |
|---|---|---|---|---|
| 1 | copper | 1.7 | 10 | 3.2 |
| 2 | copper | 1.7 | 10 | 1.6 |
| 3 | copper | 1.7 | 20 | 3.2 |
| 4 | copper | 1.7 | 20 | 1.6 |
| 5 | nickel silver | 33 | 10 | 3.2 |
When a Wheatstone bridge is balanced, current flows through the branch with Rx and R2 and current flows through the branch with R3 and R4. The same voltage is applied across both branches. Since the ration Rx/R2 equals the ratio R3/R4, points A and B are at the same potential and no current flows through the meter.
If the ratios are not the same, points A and B are at different potentials and a small current flows through the meter, causing a nonzero reading.