Question

The masses of 3 wires are in the ratio 1:2:3 and their lengths are in the ratio 3:2:1 . Then what is the ratio of their resistances

Answer 1

Answer:

Given-masses=1:2:3,

lenghts-3:2:1.            

Now, Resistance=ρ(l/a)......................(3)

We know that volume=mass/density=Area×lenght...........(1)

Area=volume/lenght,...............(2)

substitute 1 in 2.

Area=mass/density*lenght................. Substitute in 3.

∴ρ{(Lenght²×density)/mass}

Now, ratio of R₁:R₂:R₃=[ρ{(Lenght₁²×density)/mass₁}]/[ρ{(Lenght₂²×density)/mass₂}]/[ρ{(Lenght₃²×density)/mass₃}].

Since we used a same metal( if not, we assume it), ρ and density will be the same!!

Here, i didnt use symbols, so it looks complicated....but its not!

Simplyfing the ratio, we Get:

(lenght₁²/mass₁)/(lenght₂²/mass₂)/(lenght₃²/mass₃).

Substitute the values given in the question.....

You will get

9/1:4/2:1/3.

Further simplifying the ratio (lol, so much simplification)

answer=27:6:1.

HOPE IT HELPS :D