Question

resistance of a metal wire of length 1m is 26ohm at 20 C .if the diameter of the wire is 0.5 mm what will be the resistivity of the metal at that temperature​

Answer 1

Answer:

Explanation:

Resistance , R = 26Ω

Length of wire , L = 1m

diameter of circular part of wire ,d = 0.5mm = 0.5 × 10⁻³m

so, base area of wire , A = πr² = πd²/4 [ ∵d = 2r]

= 3.14 × (0.5× 10⁻³)²/4m²

= 3.14 × 25 × 10⁻⁸/4 m²

= 78.5/4 × 10⁻⁸ m² = 19.625 × 10⁻⁸ m²

Now, use formula,

R = ρL/A

Here, R is the resistance, ρ is the resistivity , L is the length of wire and A is the base area of it .

So , ρ = RA/L = 26Ω × 19.625 × 10⁻⁸m²/1m

ρ = 5.1025× 10⁻⁶ Ωm

Hence, resistivity is 5.1025 × 10⁻⁶ Ωm at 20°C

Answer 2

Answer:

Explanation:

R=26 ohm

ρl/A=26

ρ×1/π(0.25×10^-3)^2=26

ρ=26×π(0.25×10^-3)^2

ρ=5.10 ohm meter