OpenStax College Physics, Chapter 21, Problem 32 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. We are going to apply the Loop rule to the loop in this circuit that begins at point a and then goes to point e and then d, c, b and a. So we are traversing the loop in this direction— and I will just highlight the loop in yellow here— we are going to the right through this branch here and we are going to be traversing this resistor R 1 in the opposite direction to the current through it I 1 and when we do that, the potential difference will be positive so there's a plus here... a positive I 1 times R 1 and then we continue up this part of the circuit to point d and then across this resistor r 1 to point c and again we are traversing in the opposite direction to the current through it, which is I 2, and so it's gonna be a positive change in potential so that's I 2 times r 1 and then we traverse this battery— this emf 1— from the positive terminal to the negative terminal so that is a drop in potential and that means we have minus emf 1 here and then we continue along back to point a by traversing resistor R 2 and by traversing it in the downward direction, which is opposite to the upwards current, and so it's a positive I 2 times R 2 change of potential there and all of this, after you finish the loop, has to equal zero.