An aerospace engineer is investigating the resistivity of a new alloy filament for a satellite's thermal regulation system. The experimental setup consists of a DC power supply with e.m.f. EEE and internal resistance RintR_{\text{int}}Rint, connected in series with an ammeter and a length LLL of the alloy filament. The filament has a uniform circular cross-section of radius aaa and resistivity ρ\rhoρ.
The relationship between the reciprocal of the current 1/I1/I1/I and the length of the filament LLL is given by:
1I=(ρπEa2)L+RintE \frac{1}{I} = \left(\frac{\rho}{\pi E a^2}\right) L + \frac{R_{\text{int}}}{E} I1=(πEa2ρ)L+ERintThe engineer measures the supply's e.m.f. as E=5.00±0.15 VE = 5.00 \pm 0.15\text{ V}E=5.00±0.15 V and the filament's radius as a=0.150±0.003 mma = 0.150 \pm 0.003\text{ mm}a=0.150±0.003 mm.
From a plot of 1/I1/I1/I against LLL, the following parameters are determined:
Calculate the resistivity ρ\rhoρ of the alloy filament using the gradient of the line of best fit. Give your answer to an appropriate number of significant figures.
Determine a value for the internal resistance RintR_{\text{int}}Rint of the power supply and its absolute uncertainty.
