Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.

Solution

Physics sir · 4 steps

A standard resistor must keep its value as the room warms up, and that is exactly what a tiny α buys you.

1. What a standard needs. A standard resistance coil is the reference that other resistances are compared against. Its value must stay the same even when the room temperature changes or the coil warms up because current flows through it.

   R_T = R₀(1 + α Δ T)

2. Role of alpha. The change in resistance is R₀ α Δ T. For copper α ≈ 4 × 10⁻³ K⁻¹, while for manganin and constantan it is only about 10⁻⁵ K⁻¹, a few hundred times smaller. So their resistance hardly changes with temperature.
3. Other helpful properties. These alloys also have a fairly high resistivity, so a short length of wire gives a useful resistance. But the deciding property for a standard is the small temperature coefficient.
4. So. A is true, R is true, and R is the reason these alloys are chosen for standard coils. The answer is (a).

The idea to keep. Whenever a resistor must hold a fixed value, as in standard coils, potentiometer wires and meter bridge wires, look for a material with a very small temperature coefficient of resistance, like manganin or constantan.

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