Question

Calculate the resistivity of a metallic wire of length 1 m and diameter of 0.5mm and resistance is 10 ohm

Answer 1

Given :-

▪ Length of wire = 1m

▪ Diameter of wire = 0.5mm

▪ Resistance of wire = 10Ω

To Find :-

▪ Resistivity of wire.

Concept :-

▪ Resistivity is materialistic property of material, it doesn't depend upon length or area of conductor.

▪ Formula of resistance in terms of resistivity, length and area is given by

$\underline{\boxed{\bf{\pink{R=\rho\times\dfrac{l}{A}}}}}$

Calculation :-

$\implies\sf\:R=\rho\times\dfrac{l}{\pi{r}^2}\\ \\ \implies\sf\:10=\rho\times\dfrac{1}{3.14\times (0.25\times 10^{-3})^2}\\ \\ \implies\boxed{\bf{\purple{\rho=1.96\times 10^{-6}\:\Omega{m}}}}$

Answer 2

Aɴꜱᴡᴇʀ

${\sf{\large{\rho=1.96\times 10^{-6}\:\Omega{m}}}}$

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Gɪᴠᴇɴ

☞ Length of wire = 1m

☞ Diameter of wire = 0.5mm

☞ Resistance

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ᴛᴏ ꜰɪɴᴅ

➬ Resistivity of wire?

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Sᴛᴇᴘꜱ

➤ Formula of resistance in terms of resistivity, length and area is given by

$\underline{\boxed{\bf{\red{R=\rho\times\dfrac{l}{A}}}}}$

Substituting the given values,

$</p><p>\begin{lgathered}\leadsto\tt\:R=\rho\times\dfrac{l}{\pi{r}^2}\\ \\ \leadsto\tt\:10=\rho\times\frac{1}{3.14\times (0.25\times 10^{-3})^2}\\ \\ \leadsto{\tt{\pink{\rho=1.96\times 10^{-6}\:\Omega{m}}}}\end{lgathered}$

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