This question is about electric circuits and the electrical properties of materials.
State Kirchhoff’s second law and the physical quantity that is conserved according to this law.
The S.I. base units for resistance (Ω\OmegaΩ) are kg m2s−3A−2\text{kg m}^2 \text{s}^{-3} \text{A}^{-2}kg m2s−3A−2. Use the equation for electrical resistivity:
ρ=RAL \rho = \frac{R A}{L} ρ=LRAto determine the S.I. base units for resistivity ρ\rhoρ.
A researcher investigates the electrical properties of a uniform graphite rod using a circuit in which the length LLL of the rod connected in series with a cell of e.m.f. EEE and internal resistance rrr is varied. The researcher plots a graph of 1I\frac{1}{I}I1 on the vertical axis against the connected rod length LLL on the horizontal axis, where III is the current.
Show that the relationship between 1I\frac{1}{I}I1 and LLL is given by:
1I=rE+ρAEL \frac{1}{I} = \frac{r}{E} + \frac{\rho}{A E} L I1=Er+AEρLwhere ρ\rhoρ is the resistivity of the graphite rod and AAA is its cross-sectional area.
In this experiment, the cell has an e.m.f. of 1.5 V1.5\text{ V}1.5 V and the uniform graphite rod has a diameter of 0.80 mm0.80\text{ mm}0.80 mm. The straight line of best fit on the graph has a gradient of 4.50 A−1 m−14.50\text{ A}^{-1}\text{ m}^{-1}4.50 A−1 m−1. Determine the resistivity ρ\rhoρ of the graphite.
The researcher later realizes that there was a systematic error: the crocodile clip used to connect the circuit to the rod had a constant, non-zero contact resistance. Explain why this systematic error does not affect the value of the resistivity calculated in (ii).
