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A 12 cm wire is given a shape of a right angled triangle ABC having sides 3 cm, 4 cm and 5 cm as shown in the figure. The resistance between two ends (AB, BC, CA) of the respective sides are measured one by one by a multi-meter. The resistances will be in the ratio of

1. 3 : 4 : 5
2. 9 : 16 : 25
3. 27 : 32 : 35
4. 21 : 24 : 25

Correct answer: 3 : 4 : 5

Solution

The resistance of a wire is directly proportional to its length, as per the formula R = ρL/A (where ρ is resistivity, L is length, and A is cross-sectional area). Since the cross-sectional area and material are the same for all sides, the resistances will be proportional to the lengths of the sides. The sides are in the ratio 3:4:5, so the resistances will also be in the ratio 3:4:5.

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