Question

The resistance of a wire of length 100 cm and uniform area of cross-section 0.020 sq.cm, is found to be 2.0 ohm. Calculate specific resistance of wire.

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Answer 1

Answer :-

Specific resistance/resistivity of the wire is 4 × 10⁻⁶ Ωm .

Explanation :-

We have :-

→ Length of the wire = 100 cm = 1 m

→ Area of cross section = 0.02 cm²

→ Resistance = 2 Ω

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Firstly, let's convert the area of cross section of the wire from cm² to m² .

⇒ 1 cm² = 10⁻⁴ m²

⇒ 0.02 cm² = 0.02 × 10⁻⁴ m²

⇒ 2 × 10⁻⁶ m²

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Now, we know that :-

R = ρl/A

Where :-

• R is resistance.

• ρ is specific resistance.

• l is length of the wire.

• A is area of cross section.

Substituting values, we get :-

⇒ 2 = (ρ × 1)/2 × 10⁻⁶

⇒ ρ = 2 × 2 × 10⁻⁶

⇒ ρ = 4 × 10⁻⁶ Ωm

Answer 2

I=100cm=1m

area=0.02=0.000002m^2

specific resistance (Rxarea)/length

2×0.000002×1

=4x10^-6ohm-m