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A copper wire of $1 km$ has radius $1 mm$ . Resistivity of the copper wire is $1.72 \times 10^{- 8} Ωm$ The resistance of the wire is

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5.47 Ω

5.7 Ω

6 Ω

None of the above

answer is A.

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Detailed Solution

If a copper wire of length

1 km or 1000 m

has a radius of

1 mm or 10^{- 3} m

and resistivity

ρ = 1.72 \times 10^{- 8} Ωm

, then the resistance of the wire is

5.47 Ohms

.
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 the area of the circular cross-section. Hence, the relation can be written as

R = ρ \frac{l}{πr²}

On substituting the given values, we get the resistance as

\Rightarrow 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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