What length of copper wire of specific resistance 1-7 - 10-8- m and radius 1 mm is required so that its resistance is 1 -

Here, radius, r = 1 mm = 10^ 3 m Resistance, R = 1 Ω Resistivity, ρ = 1.7 × 10^ 8 Ω Now, R = ρ l /π r^2 ⇒ 1 = 1.7 × 10^ 8× l/3.14 × 10^ 3× 10^ 3 ∴ l = 184.7 m ...

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Standard X

Physics

Factors Affecting Resistance & How They Affect

What length o...

Question

What length of copper wire of specific resistance $1.7 \times 10^{- 8} Ω$ m and radius 1 mm is required so that its resistance is $1 Ω$

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Solution

Here, radius, $r = 1 m m = 10^{- 3} m$

Resistance, $R = 1 Ω$

Resistivity, $ρ = 1.7 \times 10^{- 8} Ω$

Now, $R = \frac{ρ l}{π r^{2}} \Rightarrow 1 Ω = \frac{1.7 \times 10^{- 8} \times l}{π (1 \times 10^{- 3})^{2}}$

$∴ l = 184.7 m$

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Factors Affecting Resistance & How They Affect

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What length of copper wire of specific resistance 1.7×10−8Ω m and radius 1 mm is required so that its resistance is 1Ω

Here, radius, r=1 mm=10−3 m Resistance, R=1 Ω Resistivity, ρ=1.7×10−8 Ω Now, R=ρlπr2⇒1Ω=1.7×10−8×lπ(1×10−3)2 ∴l=184.7 m

What length of copper wire of specific resistance $1.7 \times 10^{- 8} Ω$ m and radius 1 mm is required so that its resistance is $1 Ω$

Here, radius, $r = 1 m m = 10^{- 3} m$

Resistance, $R = 1 Ω$

Resistivity, $ρ = 1.7 \times 10^{- 8} Ω$

Now, $R = \frac{ρ l}{π r^{2}} \Rightarrow 1 Ω = \frac{1.7 \times 10^{- 8} \times l}{π (1 \times 10^{- 3})^{2}}$

$∴ l = 184.7 m$