Determination of resistivity (CP3)
Determine the resistivity of a metal wire by measuring its resistance at different lengths.
Apparatus
- Resistance wire (e.g. nichrome) ~1 m long
- Micrometer screw gauge
- Ammeter and voltmeter
- Low-voltage DC power supply
- Crocodile clips, metre rule and connecting leads
Safety
- Keep current low to avoid overheating the wire.
- Check polarity of ammeter connections before switching on.
Method
- Measure the wire diameter d at three positions; calculate $A = \pi(d/2)^2$.
- Connect the ammeter in series and voltmeter across a measured length L of wire using crocodile clips.
- Record V and I for at least seven values of L from 0.10 m to 1.0 m; calculate $R = V/I$.
- Plot R vs L: straight line through origin with gradient $= \rho/A$.
- Calculate $\rho = \text{gradient} \times A$.
Key Variables
Independent
Wire length L
Dependent
Resistance R
Controlled
Cross-sectional area A; Temperature (low current)
Analysis and Results
- $R = \rho L/A$. Gradient of R vs L equals $\rho/A$.
- A non-zero y-intercept indicates contact resistance at the clips.
- Uncertainty in $\rho$ comes from uncertainties in the gradient and in A.
Common Errors
- Heating the wire with high current, increasing resistivity and causing a non-linear graph.
- Measuring total wire length rather than the length between crocodile clips.
- Not zeroing the micrometer before measuring diameter.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A resistance wire has diameter 0.38 mm and the gradient of its R vs L graph is $12.5$ $\Omega$ m$^{-1}$. Calculate the resistivity.
Q22 marks
The R vs L graph has a positive y-intercept. Suggest a reason for this.