Determination of resistivity (PAG 3)
Find the resistivity of a wire by measuring resistance at different lengths.
Apparatus
- Resistance wire (~1 m, e.g. nichrome)
- Micrometer screw gauge
- Ammeter and voltmeter
- Low-voltage DC power supply
- Crocodile clips and metre rule
Safety
- Keep current low to prevent the wire heating up.
- Confirm all connections before switching on.
Method
- Measure diameter d at three positions; calculate $A = \pi(d/2)^2$.
- Connect ammeter in series; voltmeter across length L of wire. Record V and I for six to eight values of L.
- Calculate $R = V/I$ for each L.
- Plot R vs L: gradient $= \rho/A$; calculate $\rho = \text{gradient} \times A$.
Key Variables
Independent
Length L
Dependent
Resistance R
Controlled
Cross-section A; Temperature (low current)
Analysis and Results
- $R = \rho L/A$. Gradient of R vs L equals $\rho/A$.
- Line should pass through the origin; a y-intercept indicates contact resistance.
- Percentage uncertainty in $\rho$ comes from uncertainties in the gradient and A.
Common Errors
- Heating the wire with high current.
- Measuring total wire length not the length between clips.
- Not zeroing the micrometer.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A wire of diameter $0.50$ mm has gradient of R vs L equal to $4.4$ $\Omega$ m$^{-1}$. Calculate the resistivity.
Q22 marks
Suggest two improvements to reduce uncertainty in the cross-sectional area measurement.