Which of the following resistivity ( ρ ) v / s temperature ( T ) curves is most suitable to be used in wire bound standard resistors?

Solution

Physics sir · 3 steps

A standard resistor must keep its value when it warms up, so look for the flattest curve.

1. What we need. A standard resistor is a reference, so its resistance must stay almost the same as the temperature changes. Since R = ρ L/A, that means ρ should hardly change with T. A high ρ also helps, because then a short length of wire gives a large resistance.

   Option	How ρ behaves	Typical material	Fit for a standard?
   (a)	Starts near zero and rises steeply	Pure metal	No, ρ changes a lot
   (b)	Falls steadily with T	Negative temperature coefficient material	No, ρ changes a lot
   (c)	Falls sharply, close to exponential	Semiconductor	No, very sensitive to T
   (d)	High, with a very small upward slope	Alloy such as manganin or constantan	Yes

2. Why alloys. Alloys such as manganin and constantan have a high resistivity and a very small temperature coefficient of resistivity. That is the nearly flat line at a high value in (d).
3. So. Curve (d) is the most suitable for wire-bound standard resistors.

The idea to keep. For standard resistors, choose a material with high resistivity and a tiny temperature coefficient. On a ρ vs T graph, that is a nearly flat line well above zero.

Answer from the NTA final answer key. Solution by PrepWiser.