# Given 2 wires of the same length and section (iron and copper), connected in parallel. Which one produces more heat?

1. The power of the heater is determined by the formula:

P = Q / τ, Q – where the amount of heat, τ – heating time.

The amount of heat released:

Qzh = Pzh * τ

Qm = Pm * τ

2. Formula for determining electrical power:

Pzh = U² / Rzh

Pm = U² / Rm

(When connected in parallel, the voltage at the ends of each wire is the same)

3. Let’s write down the expression to determine the resistivity of the wire:

ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.

Let us express R from here:

R = ρsp * l / Ssection

Rzh = ρudzh * l / Ssec

Rm = ρudm * l / Ssec

4. Substitute all this into the expression for the amount of heat:

Qzh = Pzh * τ = U² * τ / Rzh = U² * τ * Ssec / (ρudzh * l)

Qm = U² * τ * Ssection / (ρudm * l)

5. Divide Qm / Qzh:

Qm / Qzh = (U² * τ * Ssec / (ρudm * l)) / (U² * τ * Ssec / (ρudzh * l)) = (U² * τ * Ssec * ρudzh * l) / (ρudm * l * U² * τ * Ssection) = ρudzh / ρudm

6. Substitute the numbers and find the difference:

According to the reference book, resistivity: ρudzh = 9.8 ** 10 ^ -8 Ohm * m, ρudm = 1.7 * 10 ^ -8 Ohm * m.

Qm / Qzh = ρudzh / ρudm = 9.8 ** 10 ^ -8 / 1.7 * 10 ^ -8 = 5.76 times.

Answer: 5.76 times more heat will be released on a copper conductor.