 Let's solve a couple of questions on relating phasor diagrams with equations. Here we have three circuit elements A, B and C which are connected to an AC source. The voltage across each of these is given by these equations. Choose the phasor diagram that best represents the voltage at time t, and we have to choose one out of these four options. As always, pause the video and give this one a try first. Alright, hopefully you have given this a shot. Now over here, we have three circuit elements A, B and C which are connected to an AC source And we have these three equations. And in the options, we can see the phasor diagrams for each of these three circuit elements. Let's try and look at the phase of these three circuit elements and try to understand the phase difference between these circuit elements. So we can start off with any two. Let's start off with V A and V B. So phase of A, phase of circuit element A that is omega t minus pi by 2. And if we look at the phase of circuit element B, that is omega t. If you think about the phase difference between A and B, that will be delta A, delta A minus delta A minus delta B. And that comes out to be equal to, that comes out to be equal to pi, in fact minus pi by 2, minus pi by 2. So this really means that the circuit element A is lagging behind circuit element B by pi by 2 because you have a minus over here, so it means it is lagging behind. And on the phasor diagrams, we see this arrow, this curved arrow, which means that the phasors are moving in an anticlockwise direction. So if the phase difference between these two is minus pi by 2, this means that circuit element A is lagging behind circuit element B by pi by 2. Which means it should be behind, it should be below, below B by pi by 2. And that we see in options C and B, in options B and C. Now if we look at the circuit element A and C, here we can see that the phase difference, the phase difference here, so for C, this is omega t plus pi by 2. So delta A minus delta C, the phase difference here, this is omega t gets cancelled off and minus pi by 2, minus pi by 2, that is minus pi, that is minus pi. So this means that the phase difference between A and C is 180, that is pi. So they should be in opposite directions, which is what we see in option B. C and A are in opposite directions. So the right answer for this one, the right answer for this one is option B. Let's look at one more. Here we have an alternating current source supplies current i s, which is equal to i naught sine omega d to a circuit. The phasor for this current i s and the current through one of the circuit elements i l is shown in the phasor diagram below. We can see the phasor diagram over here. We need to choose the equation that best describes the current i l. So we need to choose one equation which describes this phasor diagram of i l. Now if we look at this diagram, we see that we see these angles 45 and 45, which means that the angle between i s and i l between these two vectors, this is really 90 degrees. This is really 90 degrees. And the phase for i s, delta s, this is just this is omega t. So delta l, the phase of the circuit element l, this should be either omega t plus pi by 2 or omega t minus pi by 2. We don't know if it's plus or minus right now, but we know it is plus or minus pi by 2 because this angle is 90 degrees. So that means the option could be either A or could be either C. But we also see that the phasors are rotating in an anti-clockwise manner. We see that from the arrow here. So this means that i l is really lagging behind i s. So i l, this could be omega t minus pi by 2. The phase could be omega t minus pi by 2. And now if we do delta l minus delta s, this, the phase difference comes out to be equal to, the phase difference comes out to be equal to minus pi by 2. So this means we can write i l as, we can write i l as i not l sin omega t minus minus pi by 2. And that is option C. All right, you can try more questions from this exercise in the lesson. And if you're watching on YouTube, do check out the exercise link, which is added in the description.