A negligibly small current is passed through a wire of length 15 m and uniform cross-section \( 6.0 × 10^{−7} m^{2},\) and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
A negligibly small current is passed through a wire of length 15 m and uniform cross-section \( 6.0 × 10^{−7} m^{2},\) and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
Solution and Explanation
Length of the wire, \( l =15 m \)
Area of cross-section of the wire, \(a = 6.0 × 10^{−7} m^{2}\)
Resistance of the material of the wire, R = 5.0 Ω
Resistivity of the material of the wire = ρ
Resistance is related with the resistivity as
\(R = ρ\frac{l}{A}\)
\(ρ =\frac{ RA}{l}\)
\(ρ = \frac{5 \times 6 \times 10^{-7}}{15}\)
\(ρ = 2 \times 10^{-7} Ωm\)
Therefore, the resistivity of the material is \(2 \times 10^{−7} Ω m.\)
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