# Which resistor does the capacitor charge through?

Let's say we have a really simple circuit consisting of a capacitor sandwiched between two resistors, all in series. When the switch flips, which resistor does the capacitor charge through? I feel like the intuitive answer is that it charges through the "downstream" resistor because electrons move in the opposite direction of the current, but is that the case? If it's not, then why?

I'm basically wondering which resistor value I need to use to calculate the time constant. It doesn't make sense to me that I would combine the values, but I'm wondering if I'm wrong there as well. Sorry if this is a trivial question, but I haven't been able to find an answer anywhere.

• The current flows through both resistors so use the sum of the two resistance values for the resistors in series to find the time constant. – Farcher Jan 24 '17 at 8:21
• I suspected that might be how it is, but why is that the case? Doesn't the current flow through one resistor, then hit the capacitor, then flow through the other one? Why do both affect how long it takes for the capacitor to charge? The only thing I can think of is that it takes the electrons more than one "cycle" around the circuit to "fill" the capacitor. Is that the case? I feel like I don't really understand this at all and would deeply appreciate some conceptual clarification. – Bookie Jan 24 '17 at 8:27
• I have written an answer below. – Farcher Jan 24 '17 at 8:39

The same current flows through both resistors and the capacitor at the same time.

When the capacitor is being charged, +ve and -ve charges accumulate at the same time on opposite plates of the capacitor. Electrons flow towards the -ve plate and away from the +ve plate at equal flow rates, so that it looks like they are passing through the capacitor in a continuous current.

It makes no difference if the 2 resistors are on opposite sides or the same side of the capacitor. The same current flows through each in both cases.

The electric current is not restricted to the motion of electrons coming out of the battery. It is the motion of all the electrons already in the circuit. It is like water which is already in the pipes. As soon as you turn on the tap it comes out. You don't have to wait until the water from the reservoir travels to your house, which might take an hour or more.

• Gotcha. I assume this all balances out from a current perspective because of the "positive" charges, or lack of electrons, flowing as well right? An electron flowing away from a capacitor and an electron moving towards it serve as one continuous current provided the electrons "move" in the same direction. (please correct me if I'm wrong) Thank you for the answer. – Bookie Jan 24 '17 at 8:39

Current will flow through both resistors. Remember that the charge on both plats of plate capacitor are same but of oposite sign. So if before switching the switch the capacitor was not charged, the same amount of charge should flow to each plate and thus through resistors.

• I feel like this is getting me closer to understanding, but would you mind going into more detail? I'm wondering what's going on with the electrons in this kind of situation. Edit: Are you saying that the current flows out of each terminal of the battery to the separate capacitor plates? – Bookie Jan 24 '17 at 8:32
• Yes..electrong go to one plate of capacitor and thus meke this plate more negative charged, but they go out from other plate and thus make this plate positive charged with respect to the other plate. – NonStandardModel Jan 24 '17 at 8:47

In a series circuit the order of the components does not matter so move one of the resistors to be in contact with the other ie have both resistors on the same side of the capacitor.
Thus you can use the sum of the two resistance values in your time constant equation.