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Question
A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10−7 m2, and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
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Solution
Given: Length of the wire, l = 15 m
Area of cross-section of the wire, A = 6.0 × 10−7 m2
Resistance of the material of the wire, R = 5.0 Ω
To find: Resistivity of the material of the wire ρ = ?
Formula: Resistance is related to resistivity as,
R = `ρ l/A`
ρ = `(RA)/l`
= `(5.0 xx 6.0 xx 10^-7)/15`
= `(30 xx 10^-7)/15`
= 2 × 10−7 Ω m
Therefore, the resistivity of the material is 2 × 10−7 Ω m.
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