The lengths and diameters of three wires are given below. wire length diameter wire 1 0.5 m 0.5 cm wire 2 2 m 0.25 cm wire 3 1 m 1 cm if they all have the same resistance, find the ratio of their resistivities.

The ratio reisistivity of the wires = 15.72 : 1 : 31.44

Explanation:

ρ = RA/L Equation 1

Where ρ = resistivity of the wire, R = resistance, A = cross sectional area, L = length of the wire.

Note: All the resistance are the same.

For the wire 1,

L = 0.5 m, A =πd²/4, d = 0.5 cm = 0.005 m, π = 3.143

A = 3.143(0.005)²/4 = 0.0000196 m²

ρ₁ = R(0.0000196)/0.5

ρ₁  = 0.0000393R

For Wire 2,

L = 2 m, d = 0.25 cm = 0.0025 m

A =πd²/4 = 3.143(0.0025)²/4

A = 0.0000049 m²

ρ₂  = R(0.0000049)/2

ρ₂  = 0.0000025R

For Wire 3

L = 1 m, d = 1 cm = 0.01 m

A = πd²/4 = 3.143(0.01)²/4

A = 0.0000786 m²

ρ₃  = R(0.0000786)/1

ρ₃  = 0.0000786R

Therefore,

ρ₁ : ρ₂ : ρ₃ =  0.0000393R : 0.0000025R : 0.0000786R

ρ₁ : ρ₂ : ρ₃ = 3.93 : 0.25 : 7.86

ρ₁ : ρ₂ : ρ₃ = 15.72 : 1 : 31.44

Thus the ratio reisistivity of the wires = 15.72 : 1 : 31.44

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