generally the electrical resistance of metals rises with temp, and you know or have been given a figure for resistance at one temp say R1 resistance at T1.
But you want to know how the circuit will behave at another temp T2.
If you know the coefficient that relates a change in temp to a change in resistance, normally as so many percent or a certain fraction per degree, you can deduce the resistance at the new temp.
R2 = R1(1 + C* (T2-T1)) sort of thing, if C is expressed as reciprocal degrees - it is about 4E-3 (ie..004) per degree celcius. at room temp for aluminium, so 2 might be for a 50 degree rise if you have a 20 degree figure and want it at 70c or the reverse.
re-arrange to use the letters and figures you have, not sure what a and b are in this book.
the question says to find the impedance of a Aluminum SWA taking into account the temperature change from 20C to 70C. now the change in temperature is applied only to the resistive part of the cable (x), not the reactive part (x). If you notice, the cable has a steel wire armour and with its resistive and reactive parts. the equation 70C(a+b)x0.2 is not explained in the book. I tried many combinations using the formula you provided, but I was unsuccessful. I added the resistive parts of the core and the armour, still did not get the value shown 0.0005
I found it, it is (0.0013 x 0.0013) x 0.2 = 0.00052 ohms. I added the resistive parts of the both conductor and armour and them multiplied by the temperature factor 0.2
Glad you found it. I do not have the book, and you need to allow for that when reading my explanations.
You would not generally expect the inductive part of the impedance to change much with temperature, magnetic fields are largely unaffected by heat. (though some magnetic materials lose their magnetism when hot - do not try to solder to a magnet ! )
Resistance is, as it is all about electron collisions and mean free path, and much as it would be harder to cross a crowded room if everyone is dancing and waving their arms and legs about, compared to being the same number of people but standing perfectly still, an electron experiences a harder time getting through the metal when the atoms are all jigging about more (i.e, the metal is hotter....)
In many simpler metallic structures resistance rise almost linearly with absolute temp. This is not true of complex alloys however.
