The topic of this problem is Kirchhoff's Voltage Law. The problem is, to write the mesh or loop equation associated with this single loop circuit. So in order to do that, the first thing we have to do is we have to assign a current direction so that we can then assign polarities to the voltage drops across the resistors, using the passive sign convention. The passive sign convention was mentioned earlier in videos in chapter one and two, so if you need to get familiar with information related to the passive sign convention, you can look at those videos. So the first thing we do is we assign a current, and we're going to assign the current in a clockwise Direction around our single loop circuit. So if we do that, we know that through this passive sign convention, the current should enter the positive end of the voltage drops across our resistors. So we have these voltage drops assign these polarities across our resistors. Or we have a VR2 for voltage across resistor 2, VR1 across the resistor 1, and VR3 across resistor 3. Now that we have done that, we can now write our mesh, also known as loop equation, for this single loop circuit. So if we start at the lower left-hand corner of our circuit and we work our way around the circuit in a clockwise fashion, the first thing we hit is a -30 volts associated with the independent voltage source. We continue around our circuit and then we encounter the resistor. And the resistor is a positive voltage drop, + VR1. Continue past that resistor onto the next independent voltage source and it's -5 volts. Continuing around the loop to R2, we have another voltage drop, VR2. Continuing around the bottom portion of our single loop circuit, we have a -15 volts with a independent voltage source at the bottom of the circuit. And then we have one more voltage drop across VR3, and that is equal to 0. So that's our equation for this single loop circuit.
