Question

The resistance of a wire is 4 ohm. What is its new resistance, if it is stretched to thrice its original lenght?

Answer 1

We know that,
R = (rho)*length/Cross Sectional Area
Volume = Length * Cross Sectional Area

Assuming, Initial Volume = V1 & Final Volume = V2

Initial Cross Section Area = A1 & Final Cross Sectional Area = A2

Initial Length of Wire = L1 & Final Length of Wire = L2

Thus we have, L2 = 3 L1 (as 3 times streached)

Now, V2 = L2A2 & V1 = L1A1,

hence L1A1 = L2A2 (as V1=V2 volume remains same)

i.e. A2 = (L1/L2)A1
i.e. A2 = 1/3 A1

Now R2/R1 = [(rho*L2)/A2] / [(rho*L1)/A1]
putting the value of L2 & L1
R2/R1 = 3*3 = 9
R2 =9 * R1

Thus, R2 = 9 *4= 36 Ohm.Ans.