Step 1: State Faraday's first law.
Faraday's first law of electrolysis says the mass deposited at an electrode depends on how much charge passes through. We must find what mass is proportional to.
Step 2: Write the relation.
The law gives\[ w \propto Q \]where $w$ is the mass and $Q$ is the quantity of electricity, that is the charge.
Step 3: Recall what Q is.
The charge $Q$ is the current times the time, that is $Q = I t$. So both current and time matter together.
Step 4: Why not current alone.
Current alone does not fix the mass. A small current for a long time can give the same mass as a big current for a short time. So we need the product $It$.
Step 5: Why not time or resistance.
Time alone also does not fix the mass for the same reason. Resistance does not appear in the law at all, so it is not the answer.
Step 6: Final choice.
So the mass is proportional to the quantity of electricity $Q$.\[ \boxed{w \propto Q} \]