Question

Resistance of a metal wire of length 1m is 25 ohm.If diameter of wire is 0.2 mm.What will be the resistivity

of the metal at constant temperature.​

Answer 1

Answer:

Resistivity

$resistivity = resistance \times length \: \div area \\ = 25 \times \frac{1}{0.0002} \\ = 125000ohm \: metre$

Explanation:

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Answer 2

Answer:

7.85 × 10⁻⁷ Ω m

Explanation:

Resistance = R = 25

Length = l = 1 m

Diameter of wire = 0.2 mm = 2 × 10⁻⁴ m

⇒ Radius of wire = 0.1 mm = 1 × 10⁻⁴ m

Now, we know that

$\sf R = \rho \frac{l}{A}$

Where, ρ is the resistivity of the material, l is the length is metres and A is the area in m²

Here, area = πr²

⇒ 3.14 × (1 × 10⁻⁴ m)² (taking π as 3.14)

⇒ area = 3.14 × 10⁻⁸ m²

So,

$\sf 25 = \rho \frac{1}{3.14\times 10^{-8}}\\\\\implies \rho = 25 \times 3.14 \times 10^{-8}\\\\\implies \rho = 78.5 \times 10^{-8} \\\\\implies \rho = 7.85 \times 10^{-7}$

So, the resistivity of the metal is 7.85 × 10⁻⁷ Ω m