Question

A copper wire of resistivity 1.6 * 10-8 ohm meter has a cross sectional area of 20 * 10-4 cm2 . Calculate the length of this wire requires to make a 10 ohm coil.​

Answer 1

Given conditions,

Resistivity(ρ) = 1.6 × 10⁻⁸ Ω-m.

Cross-sectional Area(A) = 20 × 10⁻⁴ cm² = 20 × 10⁻⁸ m²

Resistance(R) = 10 Ω

Using the formula,

  ρ = RA/l

Thus, l = RA/ρ

Thus, l = 10 × 20 × 10⁻⁸/1.6 × 10⁻⁸

l = 10 × 200/16

l = 10 × 50/4

l = 5 × 25

l = 125 m.

Hope it helps.

Answer 2

If the diameter is doubled: original A=pie x(d/2)x(d/2) R=rhox L/(pie x(d/2)x(d/2)) if doubled,d=2d new resistance R1=rhoxL/(pie x d xd)=R/4 Therefore,the resistance becomes 1/4th of the original resistance when the diameter id doubled.