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,

Options

A. `4gt3gt1gt2`
B. `4gt2gt1gt3`
C. `1gt2gt3gt4`
D. `3gt1gt2gt4`

Answer

4

Explanation

Resistance of a wire `R =(pl )/(A)`
Where `p=` respectivity of a wire
l=length of a wire
A=area of a cross-section of a wire
Rate of energy dissipated as heat is `H=(V^(2))/(R)=(V^(2)A)/(pl)`
For a wire `1,H_(1)=(V^(2)A)/(pl)`
For a wire 2,
`H_(2)=(V^(2)A)/( (1,2p)(1.2L))=(0.694 V^(2)A)/(pL)=0.694H_(1)`
For wire 3 .
`H_(3)=(V^(2)A)/((0.9 p)(0.9L))=(1.23V^(2)A)/(plL)=1.23H_(1)`
For a wire 4.
`H_(4)-=(V^(2)A)/((p)(1.4L))=(0.666V^(2)A)/(pL)= 0.666H_(1)`
`therefore H_(3)gt H_(1)gtH_(2)gtH_(4)`.