A negligibly small current is passed through a wire of length 15 m and uniform cross-section

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?

Solution:

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

Resistivity of the material of the wire = ρ

Resistance is related with the resistivity as

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

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

$=\frac{5 \times 6 \times 10^{-7}}{15}=2 \times 10^{-7} \Omega \mathrm{m}$

Therefore, the resistivity of the material is $2 \times 10^{-7} \Omega \mathrm{m}$.

 

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