Two conductors of the same length and cross-section, made of aluminum and nichrome, were connected in parallel.

Two conductors of the same length and cross-section, made of aluminum and nichrome, were connected in parallel. In which of the conductors will the greater amount of heat be released if they are connected to the same current source? Why?

To answer which of the conductors will release more heat: in aluminum Q₁ or in nichrome Q₂, we find the values ​​of these quantities and compose their ratio. According to the Joule-Lenz law:

Q₁ = (I₁ ^ 2) ∙ R₁ ∙ t and Q₂ = (I₂ ^ 2) ∙ R₂ ∙ t;

Q₁ / Q₂ = (I₁ ^ 2) ∙ R₁ / (R₂ ∙ I₂ ^ 2).

From the condition of the problem it is known that two conductors of the same length L₁ = L₂ = L and cross-sections S₁ = S₂ = S, made of aluminum and nichrome, were connected in parallel to one current source, which means that U₁ = U₂ = U. Their resistances will be: R₁ = (ρ₁ ∙ L): S, and R₂ = (ρ ∙ L₂): S. According to Ohm’s law for the chain section: I₁ = U: R₁ and I₂ = U: R₂. Then:

Q₁ / Q₂ = R₁ ∙ (U / R₁) ^ 2) / (R₂ ∙ (U / R₂) ^ 2);

Q₁ / Q₂ = R₂ / R₁.

But R₁ = (ρ₁ ∙ L): S and R₂ = (ρ₂ ∙ L): S, where ρ₁ = 0.028 Ohm ∙ mm ^ 2 / m and ρ₂ = 1.1 Ohm ∙ mm ^ 2 / m is the resistivity of aluminum and nichrome. We get:

Q₁ / Q₂ = ρ₂ / ρ₁ or

Q₁ / Q₂ = 1.1 Ohm ∙ mm ^ 2 / m: 0.028 Ohm ∙ mm ^ 2 / m;

Q₁ / Q₂ ≈ 39.

Answer: in an aluminum conductor, about 39 times more heat will be released, since in it, due to the low resistance in parallel connection, the current will be higher.