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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?

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#### Solution

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 to resistivity as

R = `ρ "l"/"A"`

ρ = `("RA")/"l"`

= `(5 xx 6 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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