A copper wire of length 1 Km has a radius 1 mm and the resistivity of copper wire is 1.72×10-8 Ωm. The resistance of the wire is [[1]] Ohms.

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A copper wire of length $1 Km$ has a radius $1 mm$ and the resistivity of copper wire is $1.72 \times 10^{- 8} Ω m$ . The resistance of the wire is [[1]] $O h ms$ .

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If a copper wire of length

1 Km

has a radius

1 mm

and resistivity,

ρ = 1.72 \times 10^{- 8} Ω m

, then the resistance of the wire is

5.47 O h ms

.
It is known that the resistance

(R)

of the conductor depends directly on the length

(l)

and the resistivity

(ρ)

of the material of the conductor. Also, the resistance

(R)

of the conductor depends inversely on the area of cross section

(A)

of the conductor. Mathematically,

R = ρ \frac{l}{A}

For a wire, the cross-sectional area is that of the area of the circle. Hence, the relation can be written as

R = ρ \frac{l}{πr ²}

On substituting the given values, we get the resistance as

R = (1.72 \times 10^{- 8}) \times \frac{1000}{3.14 \times {(1 \times 10^{- 3})}^{2}}

\Rightarrow R = 5.47 Ω

Hence, the resistance of the wire is

5.47 Ω

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