Question

Two wires have the same length but one has twice the radius. Calculate (a) their relative resistance and (b) power delivered if they are identical in every other way and are connected to the same battery.

Answer 1

Resistance is given by:

R = rho*L/A

A = pi*r^2

R = rho*L/(pi*r^2)

Given that resistivity and length is same as both are made of same material, Which means resistance is inversely proportional to the square of radius

R2/R1 = (r1/r2)^2

Given that r2 = 2*r1

Then

R2/R1 = (r1/(2*r1))^2

R2/R1 = 1/4

R2 = R1/4

Part B

Now power is given by:

P = V^2/R

Since they are connected to same, battery, So power is inversely proportional to resistance

P2/P1 = R1/R2

from Part A, we know that

R1/R2 = 4

So

P2/P1 = 4

P2 = 4*P1

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