Question

The resistance of a copper wire and an iron wire at 20°c are 4.1ohm and 3.9ohm ,respectively. Find the temperature at which the resistance of both are equal

Answer 1

you didn't mention about Temperature coefficient of copper and iron. well it is an experimental value.

so, from experimental data,

temperature coefficient of copper, $\alpha_{cu}=3.9\times10^{-3}$/°C

temperature coefficient of iron, $\alpha_{Fe}=5\times10^{-3}$

given, The resistance of a copper wire and an iron wire at 20°c are 4.1ohm and 3.9ohm respectively.

Let at temperature T , resistance of copper wire = resistance of iron wire

using formula, $R=R_0(1+\alpha\Delta T)$

for copper wire , $R=4.1[1+\alpha_{cu}(T-20)]$

for iron wire , $R=3.9[1+\alpha_{Fe}(T-20)]$

now, $4.1[1+\alpha_{cu}(T-20)]=3.9[1+\alpha_{Fe}(T-20)]$

or, 4.1[1 + 3.9 × 10^-3(T - 20)] = 3.9[1 + 5 × 10^-3(T - 20)]

or, 4.1 - 3.9 = 3.9 × 5 × 10^-3(T - 20) - 4.1 × 3.9 × 10^-3(T - 20)

or, 4.1 - 3.9 = (5 - 4.1) × 3.9 × 10^-3(T - 20)

or, 0.2 = 0.9 × 3.9 × 10^-3 (T - 20)

or, 200/(3.51) = T - 20

or, T = 20 + 56.98 = 76.98 ≈ 77°C

hence, answer should be 77°C .

Answer 2

Answer:

    68

Explanation:

Research from the web