Answer:
The ratio of temperature change of nichrome wire to the temperature change of aluminum wire is found to be <u>9.75</u>
Explanation:
The change in resistances and initial resistances of the wires are:
Change in Resistance of Nichrome Wire = ΔR₁
Change in Resistance of Aluminum Wire = ΔR₂
Initial Resistance of Nichrome Wire = R₁
Initial Resistance of Aluminum Wire = R₂
Also, it is given that the change in resistance and initial resistance of both wires is equal. Therefore,
ΔR₁ = ΔR₂ ---------- eqn (1)
R₁ = R₂ ---------- eqn (2)
The change in Resistance due to temperature is given by formula:
ΔR = R α ΔT
Therefore, eqn (1) becomes:
R₁ α₁ ΔT₁ = R₂ α₂ ΔT₂
using eqn (2):
α₁ ΔT₁ = α₂ ΔT₂
ΔT₁/ΔT₂ = α₂/α₁
where,
α₁ = Temperature coefficient of resistance of nichrome = 0.4 x 10⁻³ °C⁻¹
α₂ = Temperature coefficient of resistance of aluminum = 3.9 x 10⁻³ °C⁻¹
Therefore,
ΔT₁/ΔT₂ = (3.9 x 10⁻³ °C⁻¹)/(0.4 x 10⁻³ °C⁻¹)
<u>ΔT₁/ΔT₂ = 9.75</u>
