How emf of a cell depends on the nature of electrodes and electrolyte?
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If by EMF you mean the ideal, thermodynamically determined, voltage then the answer is that increasing the surface area does not affect voltage/EMF. If by EMF/Voltage, the questions means operational voltage then it will increase because increasing the surface area of electrodes decreases the overpotential losses (Tafel equation) by essentially decreasing the resistance due to the kinetics of the reaction thus increasing operational/real voltage of a cell.
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