Question

At what temperature will a 10cm long Tungsten (W) wire with a cross sectional area of 1.5mm², have the same resistance as a room temperature, 30cm long Copper (Cu) wire with a cross sectional area of 0.5mm²?

Answer 1

The Tungsten wire and the Copper wire will never have the same resistance.

Step-by-step explanation:

To find the temperature at which the Tungsten wire has the same resistance as the room temperature Copper wire, we can use the formula for resistance:

R = ρ * (L/A)

Where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

We can rearrange the formula to solve for ρ:

ρ = R * (A/L)

Now, let's substitute the values we know. The resistivity of Copper at room temperature is 1.68 × 10^-8 Ω·m, the length of the Copper wire is 30 cm, the area of the Copper wire is 0.5 mm², and the resistance of the Copper wire is unknown.

Using the given values, we can solve for the resistivity of Copper:

ρ = R * (A/L)

1.68 × 10^-8 Ω·m = R * (0.5 mm² / 30 cm)

Now, let's solve for R:

R = (1.68 × 10^-8 Ω·m) * (30 cm / 0.5 mm²)

Finally, we can use the same formula to solve for the temperature at which the Tungsten wire has the same resistance as the Copper wire. The resistivity of Tungsten is 5.6 × 10^-8 Ω·m, the length of the Tungsten wire is 10 cm, the area of the Tungsten wire is 1.5 mm², and the resistance of the Copper wire is unknown:

R = (5.6 × 10^-8 Ω·m) * (1.5 mm² / 10 cm)

Now we can equate the two resistances and solve for the temperature:

(1.68 × 10^-8 Ω·m) * (30 cm / 0.5 mm²) = (5.6 × 10^-8 Ω·m) * (1.5 mm² / 10 cm)

(1.68 × 10^-8) / (0.5 x 10^-6) = (5.6 × 10^-8) / (10 x 10^-4)

Simplifying the equation, we get:

3.36 x 10^-2 = 0.56 x 10^-2

3.36 = 0.56

This equation is not true, which means that the two wires will never have the same resistance.