Question

A 12 cm wire is given a shape of a right angled triangleABC having sides 3cm , 4cm, and 5cm. The resistance between two ends of the respective sides are measured one by one by a multimeter. The resistances will be in the ratio of

Answer 1

Let
Resistance of 3 cm wire = 3x
​​Resistance of 4 cm wire = 4x
Resistance of 5 cm wire = 5x

Reading across 3 cm wire:
4x and 5x are in parallel= (4x) (5x) / (4x+5x) =20x/9
20x/9 and 3x are in series=20x/9 + 3x
=47x/9

Reading across 4 cm wire: 3x and 5x are in parallel= (3x) (5x) / (3x+5x) =15x/8
12x/7 and 4x are in series=12x/7 + 4x
=40x/7


Reading across 5 cm wire: 3x and 4x are in parallel= (3x) (4x) / (3x+4x) =12x/7
15x/8 and 5x are in series=15x/8 + 5x
=55x/8

Ratio of readings = 47x/9 : 40x/7 : 55x/8
=47/9 : 40/7 : 55/8
=2632 : 2880 : 3465