Question

Three cylindrical wires of same material are connected to a battery. If the ratio of length of wires is 1:2:3 and ratio of their area of cross section is 2:4:1, then the ratio of power consumed by them in series combination and in parallel combination is respectively

Answer 1

let the 3 wires be A,B,C
let the length of the 3 wires be x,2x,3x respectively
let the area of cross section of 3 wires be 2y,4y,y respectively
let R1,R2,R3 be the 3 values of the 3 wires respectively
since all 3 wires are made up of same material they have same resistivity r
from definition of resistance
R1=r×x/2y
R2=r×2x/4y
R3=r×3x/y

let powers be P1,P2,P3

In case of series,
P1:P2:P3=r×x/2y:r×2x/4y:r×3x/y (since current is constant and P=I^2×R)

P1:P2:P3=1:1:6

In case of parallel, potential difference is constant,
P1:P2:P3=2y/r×x:4y/r×2x:y/r×3x
(since P=V^2/R)

P1:P2:P3=6:6:1