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