Four wires of the same diameter are connected, in turn, between two points maintained at a constant potential difference, Their resistivities and leng

Question

Four wires of the same diameter are connected, in turn, between two points maintained at a constant potential difference, Their resistivities and leng

Four wires of the same diameter are connected, in turn, between two points maintained at a constant potential difference, Their resistivities and lengths are, `rho and L ("wire 1") 1.2rho and 1.2L("wire 2"), 0.9 rho and 0.9L("wire 3") and rho and 1.5L ("wire 4")`. Rank the wires according to hte rates at which energy is dissipated as heat, greatest first,
A. `4 gt 3 gt 1 gt 2 `
B. `4 gt 2 gt 1 gt 3 `
C. `1 gt 2 gt 3 gt 4`
D. `3 gt 1 gt 2 gt 4`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
Resistance of wire, `R=(rhol)/(A)`
Rate of energy dissipated as heat is `H=(V^(2))/(R )=(V^(2)A))/(rhol)`
For a wire, `H_(1)=(V^(2)A)/(rhoL)`
For, a wire 2,
`H_(2)=(V^(2)A)/((1.2rho)(1.2L))=(0.694v^(2)A)/(rhoL)=0.0694H_(1)`
For a wire 3, `H_(3)=(V^(2)A)/((0.9rho)(0.9L))=(1.23V^(2)A)/(rhoL)=1.23H_(1)`
For a wire 4, `H_(4)=(V^(2)A)/((rho)(1.5L))=(0.666V^(2)A)/(rhoL)=0.666H_(1)`
`therefore H_(3) gt H_(1) gt H_(2) gt H_(4)`