Answer
We can rank the wires according to the rate at which energy is transferred to thermal energy within them:
$C \gt A \gt B$
Work Step by Step
We can write an expression for the rate at which energy is transferred to thermal energy:
$Power = i^2~R$
$Power = \frac{V^2}{R}$
$Power = \frac{V^2}{\rho~L/A}$
$Power = \frac{V^2~A}{\rho~L}$
Note that the potential difference $V$ is equal for all three wires.
Note that the cross-sectional area $A$ is equal for all three wires since they have the same diameter.
We can find an expression for the power in each wire:
Wire A: $~~Power = \frac{V^2~A}{\rho~L}$
Wire B: $~~Power = \frac{V^2~A}{(1.2\rho)~(1.2L)} = 0.69~\frac{V^2~A}{\rho~L}$
Wire C: $~~Power = \frac{V^2~A}{(0.9\rho)~(L)} = 1.1~\frac{V^2~A}{\rho~L}$
We can rank the wires according to the rate at which energy is transferred to thermal energy within them:
$C \gt A \gt B$
