Question

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

Answer 1

Length of wire = 100 cm Linear resistance = 1 ohm/cm   Resistance of wire = 100×1 = 100 ohm   If it is cut into two parts, Let one part = x cm Resistance = x ohm Resistance of other part = (100-x) ohm   When they are in parallel, the effective resistance is 24 ohm   1/x + 1/(100-x) = 1/24   Or [(100-x) + x] × 24 = x(100-x)   Or 2400 = 100x - x^2   Or x^2 - 100x + 2400 = 0   Or x^2 - 60x - 40x + 2400 = 0   Or (x-60)(x-40) = 0   Or x = 40 or 60   If x = 40,   100-x = 60   Length of the two parts are 40cm and 60cm

Answer 2

here is your answer OK


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

So its answer your question......