In household wiring, long wire $2.05 m m$ in diameter is often used. Find the resistance of a $35.0 m$ long wire. The specific resistance of the wire which is made up of copper is $1.72 \times 10^{- 8} Ω - m$ .

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Solution

Resistance of a wire is given by $R = ρ \frac{L}{A}$

Given, specific resistance $ρ = 1.72 \times 10^{- 8} Ω - m$
length $l = 35 m$
diameter $d = 2.05 m m$
Hence, radius $r = \frac{d}{2} = 1.025 m m = 1.025 \times 10^{- 3} m$

$A = π r^{2} = π \times {1.025}^{2} \times 10^{- 6} m^{2} R = \frac{1.72 \times 10^{- 8} \times 35}{π \times {1.025}^{2} \times 10^{- 6}} Ω = 0.182 Ω$

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In household wiring, long wire 2.05 mm in diameter is often used. Find the resistance of a 35.0 m long wire. The specific resistance of the wire which is made up of copper is 1.72×10−8Ω−m.

Resistance of a wire is given by R=ρLAGiven, specific resistance ρ=1.72×10−8Ω−mlength l=35mdiameter d=2.05 mmHence, radius r=d2=1.025 mm=1.025×10−3 mA=πr2=π×1.0252×10−6m2R=1.72×10−8×35π×1.0252×10−6Ω=0.182 Ω

In household wiring, long wire $2.05 m m$ in diameter is often used. Find the resistance of a $35.0 m$ long wire. The specific resistance of the wire which is made up of copper is $1.72 \times 10^{- 8} Ω - m$ .