Resistance of metal wire of length 2 m is 28 Ω at 20°C. If the diameter of the wire is 0.04 mm, then what will be the resistivity of the metal at that temperature?

The resistivity of the metal wire at 20°C is approximately 1.76 × 10^-8 Ω m. This was calculated using the resistance formula and finding the cross-sectional area of the wire. The diameter of the wire was converted to meters to compute the resistivity accurately.
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Answered by Anonymous | 2025-07-04

To find the resistivity of the metal at 20°C, we can use the formula for resistance:
R = A ρ ⋅ L ​
Where:

R is the resistance of the wire, which is given as 28 Ω.
ρ is the resistivity of the metal, which is what we need to find.
L is the length of the wire, given as 2 m.
A is the cross-sectional area of the wire.

First, we need to find the cross-sectional area A of the wire. The diameter d of the wire is given as 0.04 mm. We can convert this to meters:
d = 0.04 mm = 0.04 × 1 0 − 3 m = 4 × 1 0 − 5 m
The cross-sectional area A of a wire with a circular cross-section can be found using the formula:
A = π ( 2 d ​ ) 2
Substitute the diameter:
A = π ( 2 4 × 1 0 − 5 ​ ) 2 = π ( 2 × 1 0 − 5 ) 2
A = π × 4 × 1 0 − 10
A ≈ 12.57 × 1 0 − 10 m 2
Now, substitute the known values into the resistance formula to find ρ :
28 = 12.57 × 1 0 − 10 ρ ⋅ 2 ​
Solving for ρ :
ρ = 2 28 × 12.57 × 1 0 − 10 ​
ρ = 2 351.96 × 1 0 − 10 ​
ρ = 175.98 × 1 0 − 10
ρ ≈ 1.76 × 1 0 − 8 Ωm
Thus, the resistivity of the metal at 20°C is approximately 1.76 × 1 0 − 8 Ωm . This answers the question by calculating the required property (resistivity) using a step-by-step approach.

Answered by danjohnbrain | 2025-07-06