A hollow cylindrical conductor has length of $3.14 m$ , while its inner and outer diameters are $4 mm$ and $8 mm$ respectively. The resistance of the conductor is $n \times 1 0^{- 3} Ω$ .
If the resistivity of the material is $2.4 \times 1 0^{- 8} Ω m$ . The value of $n$ is _____.

Question

A hollow cylindrical conductor has length of $3.14 m$ , while its inner and outer diameters are $4 mm$ and $8 mm$ respectively. The resistance of the conductor is $n \times 1 0^{- 3} Ω$ .

If the resistivity of the material is $2.4 \times 1 0^{- 8} Ω m$ . The value of $n$ is _____.

TestHub · Accepted Answer

Resistance of a conductor with uniform cross-section is given by,

$R = ρ \frac{l}{A}$

In this case the cross-sectional area is $π (b^{2} - a^{2})$ .

Therefore,

$R = ρ \frac{l}{π ( b ^{2} - a ^{2} )} = \frac{( 2.4 \times 1 0 ^{- 8} ) \times 3.14}{3.14 \times [ ( 4 ^{2} - 2 ^{2} ) \times 1 0 ^{- 6} ]} = 2 \times 1 0^{- 3} Ω$

Hence, $n = 2$ .

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