Question

Nichrome wire of length L and radius r has resistance of 10 ohms . How would the resistance of wire change when 1)only length of the wire is doubled 2)only diameter of the wire is doubled ?justify your answer


My doubt is for the second part of the question. when diameter is doubled, then how is radius doubled? shouldn't it be four times because d =2r? hence shouldn't the resistance be 16 times less than that of the original resistance? Please clear this doubt.

Answer 1

d = 2r (dividing by 2 on both sides)

d/2 = r

new diameter (D) = 2d

Thus,

D/2 = R

2d/2 = R

d = R (where d is the original diameter and R is the new radius.)

R1 = $rho*\frac{l}{pi*r^{2} }$ - original resistance (i)

R2 = $rho*\frac{l}{pi*4*(r)^{2} }$ - new resistance (ii)

comparing resistances,

R1:R2 = 1:1/4 = 4:1

Answer 2

Here the resistance is one forth of earlier

This is how it is

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