Question

The resistance of a metal wire of length one metre is 25 ohm at 20 degree Celsius . if the diameter of the wire is 0.3 mm what must be the resistivity of metal at that temperature

Answer 1

Answer :1.8356 × 10⁻⁶ Ωm at 20°C

Explanation: 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

Answer 2

resistivity=

l

ra

=resistance×

l

πr

2

=25×

1

3.14×(0.3×10

−3

)

2

=25×3.14×0.09×10

−6

resistivity=7.065×10

−6

ohmmetre