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Question

Four wires of the same diameter are connected, in turn, between two points maintained at a constant potential difference. Their resistivity's and lengths are; ρ and L (wire 1), 1.2 ρ and 1.2L (wire 2), 0.9ρ and 0.9L (wire 3) and ρ and 1.5L (wire 4). Rank the wires according to the rates at which energy is dissipated as heat, greatest first.

A
4>3>1>2
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B
4>2>1>3
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C
1>2>3>4
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D
3>1>2>4
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Solution

The correct option is B 3>1>2>4
Let R1,R2,R3 and R4 be the resistance of wire 1,2,3, and 4 respectively. and H1,H2,H3 and H4 be the energy dissipated by the wires respectively

R1=ρlAR2=1.2ρ×1.2lA=1.4ρlAR3=0.9×0.9ρlA=0.81ρlAR4=ρ×1.5lA=1.5ρlA

Since, HR and R3>R1>R2>R4

Therefore, H3>H1>H2>H4

Correct option is (D).

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