Resistivity

Please see the attached file for full problem description.

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A. Electrical resistivity of metals

Using an ammeter/voltmeter method determine the electrical resistivity of the given alloy and hence identify the alloy. Write up your experiment as a laboratory report. Include an estimate of the uncertainty in your readings: one example per quantity measured will suffice. My readings are :-

wire at 100cm wire at 75cm wire at 50cm
voltmeter (v) ampmeter (i) v/i ampmeter (i) v/i ampmeter (i) v/i
1 0.05 20 0.08 12.5 0.11 9
1.25 0.07 17.8 0.09 13.89 0.14 8.9
1.5 0.08 18.7 0.12 12.5 0.17 8.8
1.75 0.09 19.4 0.13 13.46 0.2 8.75
2 0.11 18 0.15 13.35 0.24 8.33
2.25 0.12 18.75 0.17 13.24 0.25 9
2.5 0.14 17.8 0.19 13.26 0.28 8.9
2.75 0.15 18.3 0.21 13.05 0.31 8.87
3 0.16 18.7 0.23 13.05 0.34 8.8


B. Electric resistivity of human tissues

This part of the assignment draws heavily for its content on various papers published in a relatively recent scientific journal. Exact references will be given after the assignment

In metals resistivity is determined by the concentration of the charge carriers ( electrons) and their average mobility. Biological tissues also have the capacity to conduct electric current. In general this property is characterised by the resistivity (Ρ) or its inverse the conductivity (σ) of the tissue. Knowledge of the resistivities of various tissues is of a basic concern to the study of bioelectric phenomena. In biological tissues, an electric current is the result of an electric field induced motion of various ions in the intra-and intercellular aqueous electrolyte. The conductivity of the tissues is mainly determined by the mobility and molar concentration of the in ions in the aqueous electrolyte, but is also possibly affected by frictional interactions of ions with membrane surfaces, dissolved macromolecules and cytoskeletal materials. The most important ionic species present being the electrolytes Na, K and Cl. Homeostatic mechanisms in the body keep the various ion concentrations constant within very strict limits. These limits may be perturbed in a variety of clinically important conditions, including dehydration and dialysis. For example the normal range of blood sodium in man is135 to 145 mM, although concentrations as low as 110mM occur with inappropriate antidiuretic hormone secretion whilst concentrations may rise to 155mM in dehydration. In an investigation of ionic shifts in dialysis an observed increase in plasma sodium of3.5% was associated with the decrease in extracellular resistivity of 2.3% and intracellular resistivity of 3.7%

A careful comparisison of various reviews of resistivity demonstrates the presence of considerable difference between resistivities reported for the same kind of tisues. These reflect a lack of consensus about the resistivities of biological tissues. The differences may occur for instance because  of a)errors in the measurement sort up b) errors in the method used to calculate resistivity from actual data, c)differences in the tissue preparation and conditioning, and d) inter- individual differences in the (patho-) physiological state of the tissue samples. Assuming that all these errors contributed randomly over the various studies and estimate of the  real value of resistivity of a particular type of tissue  could be obtained by calculating the mean of all the reported resistivities for that particular kind of tissue. The 95% confidence interval of this mean could be used as a measure of the uncertainty of our present knowledge. A statistically significant difference between the means of the different tissues could be interpreted as an existing difference in tissue resistivity.

A) Using the format illustrated below plot on graph paper the mean and 95% confidence interval resistivities for the various human tissues given in using a log scale shown below.

105


104


103


102


10
Tissue name





1. Explain the terms mean and 95% confidence interval.
2. In a. above non overlapping confidence intervals indicate significantly different means. In which tissues are there clearly statistically significantly different in resistivity.
3. Does the plot a. above imply and equality of resistivity for say Kidney, lung, muscle.
4. Calculate and tabulate the conductivity (in mS/cm) for bone, fat, tibia (cancellous), skin, kidney, liver and muscle. Use your data to draw a scatter plot of conductivity (y- axis) against water content. Label each point plotted. Consider the given data and comment on the scatter plot.
5. the correlation coefficient (spearman) for the plot in 4 above is 0.87 ( p  0.0001). explain the meaning of the given correlation coefficient.
6. using the scatter plot as evidence what might be the reason for the low resistivities of bone and fat.
7. Suggest another possible factor for variations in conductivity of the kidney, liver and muscle tissue.
8. Express the mean and resistivity of the bone in mΩ
9. Many applications of bioelectric technology in medicine are based, implicitly, on the assumption of considerable differences between resistivities for various high-water contradict tissues. Does the data presented above contradict this view.

Table 1 the calculated means and 95% confidence intervals of resistivity of various tissues

Resistivity Ω cm
Tissue Water content nos of studies nos of resistivities mean 95% confidence intervals
fat 12.5 2 7 3850 3046-4868
kidney 78.5 2 5 211 160-278
liver 75 5 18 342 296-396
lung 81.5 1 6 157 122-202
muscle 75.5 2 7 171 135-216
skin 68 2 6 329 255-424
spleen 78.9 2 5 405 307-535
Tibia 50 1 6 464 360-597

Attached file(s):

Resistivity.doc  View File

Resistivity.doc  View File