Question

You are given a wire of length 100cm and of linear resistance of 1ohm/cm . If it is cut into two equal parts ,so they are in parallel,the effective resistance is 24ohm . The lengths of the. Two parts are?

Answer 1

let L be the length of one part then remaining part will be 100 - L
Hence the ohmic values are L and 100 - L ohms
Now being connected in parallel it effective will be (100- L) * L / 100 [ recall R1 R2 /(R1 + R2) ]
By the sum it is given as 24 ohm
Equating we get (100 - L ) * L = 2400
Or L^2 - 100 L + 2400 = 0
Solving by factorising technique we get L = 60 cm or 40 cm
One part is of length 60 cm and the other is 40 cm