= Solution
First hold the production rate fixed, so total <electric current> remains $200\,\mathrm A$. If only the impure <anode> receives a factor $10^5$ increase in accessible area, its local <current density> becomes $0.002\,\mathrm{A\,m^{-2}}$, far below $j_0=1\,\mathrm{A\,m^{-2}}$. Extrapolating the large-current <Tafel equation> would give a negative anodic <overpotential>, which is physically the wrong regime. Near equilibrium the <Butler-Volmer equation> instead gives, in the same conditional two-electron model,
$$
j\simeq j_0\frac{2F\eta}{RT},\qquad\eta_a\simeq\frac{RT}{2F}\frac{0.002}{1}\simeq2.57\times10^{-5}\,\mathrm V.
$$
\b[The <anode> activation loss nearly disappears; the 1.20 V ohmic loss does not disappear.] The <cathode> still operates close to its original transport limit if it is unchanged. The conditional kinetic model gives $V_{\rm app}\simeq1.3286$ V for anode-only enlargement. Its anodic potential returns close to 0.34 V, making retention of noble <silver> and <gold> more favorable, while less noble <nickel> dissolution and <lead sulfate> formation remain relevant.
If both active areas increase by $10^5$ and their independent mass-transfer capacity scales by the same factor, both local kinetic losses become small and the conditional prediction is about $1.20005$ V. Porous internal area does not generally multiply an external diffusion-limited flux by $10^5$: pore access, <ion> depletion, tortuosity, electrical connectivity and slime blockage must be checked. If the specified 200 A/m² is instead held per true enlarged area, total current rises to $2\times10^7$ A and the unchanged <electrolyte> resistance would give $1.2\times10^5$ V, so this is an entirely different operating condition.
\b[TODO: an unconditional revised <voltage> requires the missing cathodic law and a specified area/current/mass-transfer convention.] The robust conclusion at fixed total current is reduced local activation polarization on the genuinely accessible enlarged surface, with an unchanged ohmic floor unless cell geometry or conductivity also changes. Increased geometric area alone does not prove a proportionate decrease in <energy> cost or improved purity.
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