Question

A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (Al = 2.82  108   m; Al = 3.9  103 / C; nichrome = 1.50  106   m; nichrome = 0.40  103 / C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is

Answer 1

Answer:

The ratio of temperature change of nichrome wire to the temperature change of aluminum wire is found to be 9.75

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)

ΔT₁/ΔT₂ = 9.75