A hollow cylindrical conductor has length of $3 . 14m$ , while its inner and outer diameters are $4mm$ and $8mm$ respectively. The resistance of the conductor is $n \times {10}^{- 3}Ω$ .
If the resistivity of the material is $2 . 4 \times {10}^{- 8}Ωm$ . The value of $n$ is _____.

Question

A hollow cylindrical conductor has length of

3 . 14m

, while its inner and outer diameters are

4mm

and

8mm

respectively. The resistance of the conductor is

n \times {10}^{- 3}Ω

.
If the resistivity of the material is

2 . 4 \times {10}^{- 8}Ωm

. The value of

n

is _____.

Quantrex Academy · Accepted Answer

Correct answer: 0

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

$R = ρ\dfrac{l}{A}$

In this case the cross-sectional area is $\pi\left({b}^{2} - {a}^{2}\right)$ .

Therefore,

$R = ρ\dfrac{l}{\pi\left({b}^{2} - {a}^{2}\right)} = \dfrac{\left(2 . 4 \times {10}^{- 8}\right) \times 3 . 14}{3 . 14 \times \left[\left({4}^{2} - {2}^{2}\right) \times {10}^{- 6}\right]} = 2 \times {10}^{- 3}Ω$

Hence, $n = 2$ .

A hollow cylindrical conductor has length of 3 . 14m , while its...

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