This question is about electric circuits and the electrical properties of materials.
State Kirchhoff’s first 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 resistivity:
ρ=RAL \rho = \frac{R A}{L} ρ=LRAto determine the S.I. base units for resistivity ρ\rhoρ.
A research researcher investigates the electrical properties of a new uniform conductive polymer thread designed for smart-clothing applications. They construct a test circuit where a length LLL of the thread is connected in series with a stable cell of e.m.f. EEE and internal resistance rrr. The engineer varies the connected length LLL of the thread and records the current III in the circuit, subsequently plotting a graph of 1I\frac{1}{I}I1 on the vertical axis against the thread length LLL on the horizontal axis.
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 conductive thread and AAA is its cross-sectional area.
In this investigation, the cell has an e.m.f. of 3.3 V3.3\text{ V}3.3 V and the conductive thread has a uniform diameter of 0.24 mm0.24\text{ mm}0.24 mm. The line of best fit on the engineer's graph has a gradient of 115 A−1 m−1115\text{ A}^{-1}\text{ m}^{-1}115 A−1 m−1. Determine the resistivity ρ\rhoρ of the polymer thread.
The engineer later discovers that the zero-point on their ruler was misaligned, meaning that all measured values of LLL were recorded as 15 mm15\text{ mm}15 mm shorter than the actual physical length of thread connected in the circuit. Explain why this systematic measurement error has no effect on the value of resistivity determined in (ii).
