I have a procedural question about KVL or Kirshhoff\'s Loop Rule, as we call it.

Question

I have a procedural question about KVL or Kirshhoff's Loop Rule, as we call it. I understand that the rule is that the algebraic sum of the changes electric potential around any closed circuit loop is zero.

I understand that the potential difference across a battery is + if a positive charge goes from the positive terminal to the negative terminal and - if it goes from the negative terminal to the positive terminal. That makes sense. What I'm confused about is this: the potential difference (voltage) across a resistor is -IR if a positive charge goes across the resistor in the direction of the electric current and +IR if the charge goes across the resistor opposite the current.

Please see the circuit below. In a situation like this, isn't the current only going to be in one direction? So, since the current is only going in one direction, the voltage will be -IR across each resistor? I initially thought that in a situation when the charge goes across the battery in the opposite direction that the subsequent resistors would have a voltage of +IR because they went across the battery in a direction opposite the first battery [like in the circuit below,I thought the bottom branch would be -4V +I(60) +I(40)]. But apparently, all the resistors are -IR because that current is only going in one direction, from the positive terminal to the negative terminal?. So, is it sufficient to say if you have a circuit like the one below, ie., all the resistors are in series, the resistors are all always going to be one thing: either +IR or -IR? For example, in the circuit below, the sum of voltages would be +10V -I(20) -4V -I(60) -i(40) = 0 and after solving, the current would be 0.050A ?(ignore A and B).

Thanks for the time you took to read this!

Explanation / Answer

While moving across the resistor, potential change is equal to i*R. Please note that resistors do not have any voltage themselves. We are just calculating the potential drop or gain across them. Now current always flows from higher potential to lower potential. So if we encounter a situation in which we are going forward in the loop in the direction of flow of current, then potential drops across resistor and we assign it -i*R value (as in above example). But in more complex circuits, situation might arise when we are moving in the direction opposite to the flow of current for some resistors. In that case, as we move across the resistor, potential rises by amount i*R and hence we write +i*R in the equation. Please note that the current is always going in (and for that matter always going out) of the resistor. Its the direction in which we choose to move in the loop that matters.

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