Question

Calculate the resistance of 1 m long copper wire of radius 1 mm. Resistivity of the copper is 1.72 x 10-8 m

Answer 1

Answer:

Resistance, R = ρ l/A = ρ l/πr2

Resistance, R = ρ l/A = ρ l/πr2On substituting the values, we get

Resistance, R = ρ l/A = ρ l/πr2On substituting the values, we getR = 1.72 x 10-8 x 103/3.14 x (1 x 10-3)2

Resistance, R = ρ l/A = ρ l/πr2On substituting the values, we getR = 1.72 x 10-8 x 103/3.14 x (1 x 10-3)2= 1.72/3.14 x 10

Resistance, R = ρ l/A = ρ l/πr2On substituting the values, we getR = 1.72 x 10-8 x 103/3.14 x (1 x 10-3)2= 1.72/3.14 x 10= 17.2/3.14 = 5.47Ω

Explanation:

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Answer 2

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$\large\underline{\sf{\red{Given}}}$

✭$\sf Length\: (l) \:of \:wire = 1$

✭ $\sf Radius\: of \:wire = 1$

✭ $\sf Radius\: of \:wire\: in\: m = 10^{-3}$

✭ $\sf Resistivity\: (\rho) = 1.72\:\times\:10^{-8}\:\text{\O}mega$

$\large\underline{\sf{\blue{To\:Find}}}$

✭ $\sf Resistance\: of \:wire?$

$\large\underline{\sf{\green{Solution}}}$

Calculating area (A) of cross section of wire,

➝ $\sf A = \pi r^2$

➝ $\sf A = 3.14\:\times\:10^{-3}\:\times\:10^{-3}$

➝$\sf A = 3.14\:\times\:10^{-3-3}$

➝ $\sf A = 3.14\:\times\:10^{-3-3}$

➝ $\sf \pink{A = 3.14\:\times\:10^{-6}\:m^2}$

Calculating resistance of wire,

➳ $\sf R = \dfrac{\rho\:\times\: l}{A}$

➳ $\sf R = \dfrac{1.72\:\times\:10^{-8}\:\times\:1}{3.14\:\times\:10^{-6}}$

➳$\sf R = {\cancel{\dfrac{1.72}{3.14}}}\:\times\:10^{-8+6}$

➳ $\sf R = 0.54 \:\times\:10^{-2}$

➳ $\sf \pink{R = 0.0054\:\text{\O}mega}$

$\therefore\:{\sf{\underline{Resistance\:of\:wire = \bf{0.0054\:\text{\O}mega}}}}$

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