In this experiment, you will determine the resistivity of constantan wire. You measures the resistance R of a 1.00 m length of wire using a battery, ammeter...

(a) The three micrometer readings are: 0.38 mm, 0.36 mm, and 0.37 mm. [1]

(b) Mean diameter:

\[ d = \frac{0.38 + 0.36 + 0.37}{3} = \frac{1.11}{3} = 0.37 \text{ mm} \] [1]

(c) Cross-sectional area: [2]

\[ A = \pi \left(\frac{d}{2}\right)^2 = \pi \times (0.185)^2 = \pi \times 0.03423 = 0.1075 \text{ mm}^2 \] [1]

Converting to m\( ^2 \):

\[ A = 0.1075 \times 10^{-6} \text{ m}^2 = 1.075 \times 10^{-7} \text{ m}^2 \] [1]

Since 1 mm = 10\( ^{-3} \) m, 1 mm\( ^2 \) = 10\( ^{-6} \) m\( ^2 \).

(d) Resistance of the wire:

\[ R = \frac{V}{I} = \frac{1.15}{0.29} = 3.97 \text{ }\Omega \] [1]

(e) Resistivity of the wire: [2]

\[ \rho = \frac{R \times A}{l} = \frac{3.97 \times 1.075 \times 10^{-7}}{1.00} \] [1]

\[ \rho = 4.3 \times 10^{-7} \text{ }\Omega\text{ m} \] [1]

The accepted value for constantan is approximately \( 4.9 \times 10^{-7} \) \( \Omega \) m. The slight difference is within experimental error.

(f) Three micrometer readings are taken to detect if the diameter varies along the wire and to obtain a more reliable average. A non-uniform wire would give different values at different points. [1]

(g) To check for zero error: close the micrometer jaws with nothing between them and check that the reading is exactly zero. If it is not, note the zero error and subtract it from all subsequent readings. [1]

(h) The resolution of the micrometer is 0.01 mm. [1]

(i) Range of micrometer readings:

\[ \text{Range} = 0.38 - 0.36 = 0.02 \text{ mm} \] [1]