Question

if resistance of a wire of unit length is 26 ohm at 20 degree Celsius and its radius is 1.5 mm. find its resistivity ​

Answer 1

Given,

Length of  Wire, l = 1 m

(Note:- Unit  of  length is  not  mentioned in question, So We  have  taken as  1m)

Resistance, R = 26 ohm

Radius, r = 1.5 mm

r = 1.5 mm

r = 1.5 × 10⁻³ m

Area  of  cross section of wire = πr²
 A = 3.14 × (1.5 × 10⁻³)²
                                            A = 3.14 × 1.5 × 1.5 × 10⁻⁶

 A = 7.065 × 10⁻⁶

We know that, Resistance  of  a  wire at  constant temperature is directly proportional its  length and  inversely proportional to its  cross section area.

R ∝  l/A

R = ρl/A

Where ρ is  Resistivity of wire.

ρ = RA/l

Putting  values  of R, A and l

ρ = (26×7.065 × 10⁻⁶)/1

ρ = 183.69 × 10⁻⁶

ρ = 1.83 × 10⁻⁴  Ω - m

ρ = 1.83  × 10⁻⁴ × 10⁻²  Ω-cm

ρ = 1.83 × 10⁻⁶ Ω-cm

Answer 2

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