Question

A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will be

the length of this wire to make its resistance 10 Ω? How much does the resistance

change if the diameter is doubled?
I have done half of it plz you solve next of it......
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Answer 1

Answer:

122.66 m

Explanation:

Given :

Diameter d = 0.5 mm

Radius r = 0.25 mm = 0.25 × 10⁻³ m

Area A = ( 0.25 × 10⁻³ )² π m²

= > Area A = 0.0625 × 10⁻⁶ π m²

= > Area A = 6.25 × 10⁻⁸ π m²

Resistivity ρ = 1.6 × 10⁻⁸ Ω m

Resistance R = 10 Ω

We are asked to find length :

We know :

R = ρ L / A

= > 10 = ( 1.6 × 10⁻⁸ )  L / ( 6.25 × 10⁻⁸ π )

= > 10 = 1.6 L / 6.25 π

= > L = 62.5 × 3.14 / 1.6 m

= > L  =196.25 / 1.6 m

= > L = 122.66 m

Hence we get required answer!