Why does increasing surface area of the electrode decrease resistance? Which increases immediately if the surface area of the silver electrode is increased?
  
  
  overall cell voltage
  rate of change of $\ce{[Ag+]}$
  mass of $\ce{Cu}$ electrode
  change in ratio of electrode masses; ∆$(\frac{\text{ mass of Cu}}{\text{ mass of Ag}})$
  


The correct answer was (2), but I'm not sure why the reaction rate would go up if the surface area of the silver electrode increased. The rate of reaction is proportional to the current flowing through, which by Ohm's Law is $\frac{V}{R}$. This means that the resistance must have decreased if current increases. But resistance of the electrodes is only related to the length and cross sectional area. The problem does not specifically state any change in length or cross sectional area. It only says surface area, so what am I missing here?
Fluid flow is always an excellent analogy for understanding current flow.

Fluid flow rate -> electrical current

Pipe friction, valves and other throttlers -> electrical resistance

Fluid pressure -> voltage.

In this case, the amount of contact between the electrode and the solution is most likely the bottleneck of the circuit so increasing the area of contact should increase the current.  Similar to how cranking the valve on a faucet or outdoor spigot more and more open increases the flow rate of the water coming out.