Question

Resistance of a metal wire of length 1 m is 26 ohms at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?
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Answer 1

$\cdot$ Answer :

If the diameter of the wire is 0.3 mm, then resistivity will be 1.8356 × 10⁻⁶ Ωm at 20°C .

$\cdot$ Explanation :

We are given with, length of the wire, resistance, diameter of the wire, which measure as,

• Length = 1 m

• Resistance = 26 Ω

• Diameter = 0.3 mm = 0.3 × 10⁻³m

Before proceeding directly to the resistivity, we need to calculate the base area of the wire , which is given as,

⇛ A = πr²

⇛ πd²/4⠀ [As 2r = D]

⇛ 3.14 × {(0.3 × 10⁻³)²}/4

⇛ 3.14 × 9 × 10⁻⁸/4

⇛ 28.26/4 × 10⁻⁸

⇛ 7.06 × 10⁻⁸ m²

Now, to calculate the resistivity of the metal wire, the required formula is,

➟ R = ρL/a

➟ ρ = Ra/L

➟ ρ = 26Ω × 7.06 × 10⁻⁸

➟ ρ = 1.8356 × 10⁻⁶ Ωm

Therefore, if the diameter of the wire is 0.3 mm, then resistivity will be 1.8356 × 10⁻⁶ Ωm at 20°C .

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