Question

Resistance of a metal wire of length 1m is 26ohm at 20 degree Celsius. If the diameter of the wire is 0.3mm, what will be the resistivity of the metal at that temperature? Predict the material of the wire?

Answer 1

Answer:

l = 1 m

R = 26Ω

d = 0.3 mm = 3/1000 m

∴ r = 0.3/2000 m    

Area of cross section = π$r^{2}$

                                     = 3.14 x (0.3/2000)^2 $m^{2}$

formula, R = ρL/A

∴ρ = RA/L

     = 26 x 3.14 x0.3/2000 x 0.3/2000

     =1.8369  x  $10^{-6}$  Ωm is the resistivity of metal.

hope it will help you!!!!

Answer 2

Answer:

Resistance , R = 26Ω

Length of wire , L = 1m

diameter of circular part of wire ,d = 0.3mm = 0.3 × 10⁻³m

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

= 3.14 × (0.3 × 10⁻³)²/4m²

= 3.14 × 9 × 10⁻⁸/4 m²

= 28.26/4 × 10⁻⁸ m² = 7.06 × 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 × 7.06 × 10⁻⁸m²/1m

ρ = 1.8356 × 10⁻⁶ Ωm

Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at 20°C