Question

Calculate the resistivity of the material of a wire 1.0m long, 0.4mm in diameter and

having a resistance of 2.0 ohm​

Answer 1

$\bf{\underline{\underline{Given}}}$

$\mathsf{\star\: \: Length\: (L) = 1\:m}$

$\mathsf{\star\: \: Diameter\: (d) = 0.4\:mm}$

$\mathsf{\star\: \: Radius\: (r) = \frac{d}{2}}$

$\mathsf{\implies\: r = \frac{0.4}{2}\: mm}$

$\mathsf{\implies\: r = 0.2\: mm}$

$\fbox{\mathtt{\red{1\:mm = 10^{-3}\:m}}}$

$\mathsf{\implies\: r = 0.2 × 10^{-3} \: m}$

$\mathsf{\star\: \: Resistance\: (R) = 2\:Ω}$

$\bf{\underline{\underline{To\:find}}}$

$\mathsf{\star\: \: Resistivity \:of \:the\: wire\: ( \rho ) }$

$\bf{\underline{\underline{Solution}}}$

$\fbox{\mathtt{\blue{ Area\: _{wire} = \pi × r^{2}}}}$

$\mathtt{\implies\: A = 3.14 × (0.2 × 10^{-3})^{2}}$

$\mathtt{\implies\: A = 3.14 × 0.2 × 10^{-3} × 0.2 × 10^{-3}}$

$\mathtt{\implies\: A = 3.14 × 0.04 × 10^{-6}}$

$\mathtt{\implies\: A = 0.1256 × 10^{-6}}$

$\mathtt{\implies\: A = 125.6 × 10^{-3} \: \:m^{2}}$

We know that

$\fbox{\mathsf{\red{Resistance \: (R) = \rho \frac{L}{A}}}}$

$\mathtt{\implies\: \rho = \frac{R × A}{L}}$

$\mathtt{\implies\: \rho = \frac{2\:Ω × 125.6 × 10^{-3} \: m^{\cancel{2}}}{1\: \cancel{m}}}$

$\fbox{\mathtt{\green{ \: \rho = 251.2 × 10^{-3} \: Ω \: m} \:\:(Answer)}}$

Answer 2

Answer:

Resistance=2 ohm

Length=1m

Diameter=4 mm =4/1000=0.004m

Radius=diameter/2=0.004/2=0.002m

Resistance = resistivity×length/area

2 = resistivity×1/0.002

2×2/1000=resistivity

4/1000=resistivity

0.004= resistivity