Question

(1) A wire of 9 ohm resistance having 30cm length is tripled on itself.What is its new resistance?
(2) What length of copper wire of resistivity 1.7 x 10 to the power of -8 x ohm metre and radius 1 mm is required so that its resistance is 1 ohm?

Answer 1

(2)

p = 1.7 × 10^-8 ohm/m

A = π × 10^-6 m²

R = 1 ohm ,

since ,

R = pl/A

1 = 1.7 × 10^-8 × l / π × 10^-6

π × 10^3 / 17 = l

l = 184.799 m

Answer 2

1) R = 9 Ω        L = 30 cm        ρ = constant
     R' = ?        L' = 3 * L           

case a)
   If the length is tripled ie., multiplied by 3 , then:
       R = ρL/A,        so R is also multiplied 3 times =>  R' = 3 R  =>  27 Ω

case b)
   if  the wire is folded so that the length becomes L/3 and the area of cross section now becomes 3 times.    R' = R *1/3 * 1/3 = R/9 = 1 Ω
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2)
       R = ρ L / A    =>  L = R A /ρ
   L = 1 Ω * π * (1 * 10⁻³)²  m² / 1.7 * 10⁻⁸ Ω-m
       = 184.79 m