Question

If we apply a potential difference of 4. 50 v between the ends of a wire that is 2. 50 m in length and 0. 654 mm in radius, the resulting current through the wire is 17. 6. What is the resistivity of the wire material?.

Answer 1

According to the resistance, the resistivity of wire material is 1.37 x 10¯⁷ Ωm.

We need to know about the resistance of conductive material to solve this problem. Resistance can be defined as the ratio of the voltage applied to current flow It can be written as

R = V / I

where R is resistance, V is voltage and I is current.

The resistance of the material depends on its resistivity and follows this equation

R = ρ . L / A

where ρ is resistivity, L is the length of the material and A is the surface.

From the question above, we know that

V = 4.5 V

L = 2.5 m

r = 0.654 mm = 6.54 x 10¯⁴ m

I = 17.6 A

Find the surface area

A = π . r²

A = π . ( 6.54 x 10¯⁴ )²

A = 1.34 x 10¯⁶ m²

Find the resistivity of the wire

R = V / I

ρ . 2.5 / (1.34 x 10¯⁶)= 4.5 / 17.6

ρ = 1.37 x 10¯⁷ Ωm

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