Question

Three wires of the same diameter and length are made from three different metals: copper (rho = 1.7 × 10–8 Ω·m), aluminum (rho = 2.7 × 10–8 Ω·m), and silver (rho = 1.6 × 10–8 Ω·m). Which wire has the least resistanc

Answer 1

Answer:

Silver has least resistance

Explanation:

The given data :-

i) Since the diameter of each wire is same so the area of each wire is same i.e A₁ = A₂ = A₃.

ii) Length of each wire is same i.e L₁ = L₂ = L₃.

iii) Resistivity of copper ( ρ₁ ) = $1.7 * 10^{-8}$ Ω.m

iv ) Resitivity of aluminum (  ρ₂ ) =  $2.7 * 10^{-8}$ Ω.m

v ) Resitivity of silver ( ρ₃ ) = $1.6 * 10^{-8}$ Ω.m

Resistance is given by

$R = \frac{\rho* L }{A}$

Since the area and length are same of all three wire so it becomes constant.

R ∝  ρ

So by observing the resistivity of all three wire.

ρ₃ <  ρ₁ <  ρ₂

Therefore  the wire silver has least resistance since it has least value of resistivity.