Please help (urgent) TYVM!

Question

Wire A has a resistance of 12 2. Wire B, of the same material, is twice as long and has half the cross-sectional radius of wire A. What is the resistance of wire B?

Answer 1

R=(p*L)/A

R_a of wireA = 12 (not sure if you attempted to say 12.2, worded strange)

R_a of wireA = (p*L₁)/A₁, where L₁ is length of wire A and A₁ is cross-section of wire A

p is the same for both wires

R_b of wireB = (p*L₂)/A₂

L₂=2*L₁, since wire 2 is twice as long

A₂=πr²

where r = 0.5r₁, since wire b has half the cross-sectional radius of wire A

let's substitute back:

R_b=(p*2L₁)/(π(0.5r₁)²)

R_b=8(pL₁)/(πr₁²)

R_b=8(pL₁)/(A₁), since R_a = (p*L₁)/A₁

R_b=8R_a

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