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The resistance of a wire of length $300 m$ and cross-section area $1.0 m m^{2}$ made of material of resistivity $1.0 \times 1 0^{- 7}$ $Ωm$ is.

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2 Ω

3 Ω

20 Ω

30 Ω

answer is D.

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Detailed Solution

The relation between resistivity, area of cross section and length is
Resistivity,

ρ = \frac{R \times A}{l}

Here Resistivity,

ρ = 1.0 \times 1 0^{- 7} Ω

Area of cross-section,

A = 1.0 m m^{2}

Area

1.0 m m^{2}

will be equal to

\frac{1}{1000}

m^{2}

as,
1 meter = 1000 mm.
Length of wire,

l = 300 m

So, putting these values in the above formula, we get:

1 \times 10^{- 7} = \frac{R \times 1 \times 10^{- 3}}{300}

R = \frac{1 \times 10^{- 7} \times 300}{1 \times 10^{- 3}}

R = 30 Ω

Thus, the resistance of the wire is

30 Ω

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