Two uniform wires of same material , each weighing `1 g` but one having double the length of the other, are connected in series , carrying a current of `10 A`. The length of the longer wire is `20 cm`. Calculate the rate of consumption of energy in each of the two wires. which wire gets hotter ? The resistivity of the material of the wire is `20 xx 10^(-5) Omega cm`. (Density of material =11 units )

Explanation

Let `a_(1)` and `a_(2)` be the area of cross-section of shorter and longer wire respectively.
As, = mass = volume `xx` density `= a l rho`
`:. 1 = a_(1) xx 10 xx11 = a_(2) xx 20 xx 11`
or `a_(1) = 1/10xx11 cm^(2) and a_(2) = 1/20xx11 cm^(2)`
`:. R_(1) = 20 xx 10^(-5) xx 10/(1//(10 xx 11))`
`= 20 xx 10^(-5) xx 10 xx 10 xx 11 = 22 xx 10^(-2) Omega`
`:. R_(2) = 20 xx 10^(-5) xx 20/(1//(20 xx 11)) = 88 xx 10^(-2) Omega`
And rate of heat produced,
`H_(1) I^(2)R_(1) = (10)^(2) xx 22 xx 10^(-2) = 22 W`
and `H_(2) = I^(2) R_(2) = (10)^(2) xx 88 xx 10^(-2) = 88 W`