Question

10. Calculate the area of cross section of a wire of length 2m, its resistance is 25Ω and the resistivity of material of wire is 1.84*10-6 Ωm.

Answer 1

➤ Answer

• Area of cross section = ${0.144\times 10}^{-6}$m².

➤ Given

• Length of the wire = 2m.
• Resistance = 25Ω.
• Resistivity of material = 1.84 × 10^-6Ωm.

➤ To Find

• The area of cross section of wire.

➤ Step By Step Explanation

Given that the length of wire = 2m, its resistance is 25Ω and the resistivity of material of wire is 1.84 × 10^-6 Ωm. We need to find the area of cross section of wire.

So let's do it !!

➠ Formula Used

$\dag \underline{\boxed{ \green{\rho = \cfrac{r \times a}{l}}}}$

Where A is the area of cross section, L is the length of wire, R is the resistance. $\rho$ is the resistivity of wire.

➠ Substituting the values

$\longmapsto 25 = \cfrac{{1.8 \times 10}^{ - 6} \times 2}{a} \\ \\\longmapsto 25a = {1.8 \times 10}^{ - 6} \times 2 \\ \\\longmapsto a = \cfrac{ {1.8 \times 10}^{ - 6} \times 2 }{25} \\ \\\longmapsto a = \cfrac{1.8 \times 2}{25 \times {10}^{6} } \\ \\\longmapsto a = \cfrac{3.6}{25 \times {10}^{6} } \\ \\\longmapsto a = {0.144 \times 10}^{ - 6} {m}^{2}$

➵ Therefore, area of cross section = ${0.144\times 10}^{-6}$m².

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