The resistance of an electrolyte varies with temperature T as ${\mathrm{R}}_{\mathrm{T}}=\frac{{\mathrm{R}}_0}{1+\mathrm{\alpha T}}$, where $R_0$ and $\alpha$ are constants. A constant potential difference V is applied to the two electrodes (each of surface area A) which are dipped in this electrolyte. If T₀ it the temperature of the surroundings, the loss of heat to the surroundings per unit surface area per unit time is governed by the same relation $H=k\left(T-T_0\right)A,$ then the steady state temperature is

• A

  $\frac{\left({\mathrm{V}}^2+{\mathrm{kAR}}_0\mathrm{T}\right)}{\left({\mathrm{kR}}_0\mathrm{A}-{\mathrm{\alpha V}}^2\right)}$

• B

  $\frac{{\mathrm{V}}^2}{{\mathrm{kR}}_0\mathrm{A}-{\mathrm{\alpha V}}^2}$

• C

  $\frac{V^2}{RkA}$

• D

  None of these