Question

Q.3 There is two conductors A and B of same

material having lengths L and 2L and radii r and
r/2 respectively. What is the ratio of their
resistance?​

Answer 1

resistance = (resistivity.(l/A))

so for the 2 materials we get

r1 = resistivity.(l/r)

r2=resistivity.(2l/(r/2))

so ratio r1/r2=1/4

Step-by-step explanation:

The resistance is proportional to the length and inversely proportional to the area (which is proportional to the square of the radius). Thus if we are just comparing the two (so the constants will cancel out).

r1 = l/r^2 (r squared).

r2 = (2l)/(1/2r)^2

r2 = 2l/(1/4)r^2

dividing by 1/4 is the same as multiplying to 4, so you are multiplying by 2 and then by 4, thus by 8.

Thus R2 is 8 times more than R1.