(i) Derive an expression to show that, for a conductor whose temperature coefficient of resistivity is α and which undergoes a small temperature rise ΔT from a reference temperature, the fractional change in its resistance ΔR ⁄ R₀ is approximately αΔT.
(i) Derive an expression to show that, for a conductor whose temperature coefficient of resistivity is α and which undergoes a small temperature rise ΔT from a reference temperature, the fractional change in its resistance R0ΔR is approximately αΔT.
(ii) A manganin resistor has α=1.5×10−5∘C−1 at room temperature. Estimate the temperature rise that would cause its resistance to increase by 0.20%.
(iii) A copper resistor has α=4.0×10−3∘C−1 at the same reference temperature. For the same fractional change in resistance as in part (ii), calculate the required temperature rise.
(iv) Discuss, with quantitative reference to your results, why manganin is preferred over copper for making precision standard resistors.