Diagram (a) shows a circuit that can be used to rectify an alternating current. If the input voltage is that shown in diagram (b), which of the following graphs shows the output voltage as measured by the voltmeter in the circuit diagram?
Okay, so we’ve been given the circuit that’s used to rectify an alternating current, and we’ve been told that the input voltage look something like this. Now the input voltage is going to be from this voltage source here, and we’ve been asked to find which one of these diagrams shows the correct output voltage as measured by this voltmeter in the diagram. Now before we answer the question, let’s actually consider the circuit and what it’s meant to do. So first of all, we’ve got this AC alternating current voltage source. And as we already know, diagram (b) shows us the voltage from this voltage source because we’ve got its potential difference on the vertical axis and time on the horizontal axis. In other words, the voltage varies sinusoidally as time progresses. And then we’ve got this weird part of the circuit.
Now this pic consists of four diodes. Diodes are electrical components that will only allow current to pass through them in one direction, although unfortunately they don’t light up our world like nobody else. Anyway, so the whole point is that these diodes are set up in such a way that certain flows of current through them are restricted and other flows are allowed. We’ll study this in a little bit more detail in a second. But then we also notice that alongside this weird four-diodes set-up, we’ve got this branch of the circuit where we’ve got a resistor and a voltmeter connected in parallel with that resistor. Now it’s important to note that this curvy bit here tells us that this branch of the circuit is not connected to this branch of the circuit. And so the wires don’t actually connect with each other. The wire from this branch simply goes over the wire from this branch.
Okay so now that we’ve got that sorted, let’s consider what happens when the input potential difference is indeed as in diagram (b). Now the voltage source is going to be putting in a sinusoidal voltage to the circuit. What this means is that at some point in time, the current will be flowing in this direction. And at other points in time, it’ll be flowing in this direction because that’s exactly what we see happening in diagram (b). We can see that at this point the current is zero, but then it starts flowing in a certain direction, peaks, and then reduces again. Once it passes zero and becomes negative, this means that the current is flowing in the opposite direction. Then it becomes zero again and increases, increases in the first direction, reduces again and reaches zero, then it flows in the opposite direction, and so on and so forth.
So at time 𝑡 is equal to zero by the looks of it, current is not flowing in either direction. At this point, current is maximum in one direction, let’s say this way, so we’ll say clockwise is positive. At this point in time, current is still positive but small. Then at this point in time, there’s no current flow in either direction once again. Then at this point in time, the current is negative and fairly large, but still not at its maximum value. Then at this point, which is the peak of the graph or the trough depending on how you wanna look at it, the current is still negative or in the counterclockwise direction. But this time, it’s at its maximum possible value. And we can keep picking random points on the graph and seeing which way the current is flowing at that point in time as well as the magnitude or size of the current. But at this point, we’ve got a good idea of what’s happening at this voltage source.
So let’s consider what happens in this weird bit of the circuit when current is flowing for example in this direction. So let’s say we’re considering at this point in time. Current is maximum and positive or, in other words, flowing clockwise. So now let’s say we’re considering conventional current, and it’s flowing clockwise, and it arrives at this junction. Now at this point, it could go two ways, either along this branch or along this branch. However, we need to remember that we’re considering diodes in our circuit and that diodes only allow current to pass through them in one direction and not in the other direction. Now when we’re considering conventional current, the circuit diagram of a diode is actually quite useful, because this little arrow that forms a part of the diode shows us the direction that conventional current is allowed to flow through the diode.
In other words, this triangly bit is the arrow. That shows us the direction. And most importantly, current is not allowed to flow against this arrow. So that is not allowed. So therefore, coming back to our circuit diagram, we’ll see that current is allowed to flow through this diode, but there is no current allowed in this diode; it can’t flow. And then at this point, we reach this junction here. Now once again, the current could split this way and this way. But once again, there’s another diode there to stop it flowing in that direction. So instead, current just goes along this branch and through the resistor. Then once the current has passed the resistor, it continues flowing through this branch, and it reaches yet another junction. Now at this point, it is allowed to split and go in both directions, because both diodes are in the correct orientation.
And then the current going this way will go through this diode once again. And then this current will go this way through that diode. Now current from both of those branches will meet again at this branching point. And then this diode will prevent them from going left, so they will go right once again. Now that became all very complicated and messy. But remember, we’re trying to consider what this voltmeter is going to show as an output. And so the important bit is what happens at this resistor, because the voltmeter is measuring the voltage across that resistor. So we saw that current is flowing this way through the resistor. And because we said earlier that clockwise flowing current is positive, we can see that the voltmeter would pick up a positive voltage across that resistor.
And remember, because at this point we were considering the AC source producing maximum current. This would mean that the current through the resistor was maximum as well. And we can recall from Ohm’s law that because at that point in time the current through the resistor was maximum and of course the resistance of the resistor is fixed, the voltage would be maximum as well. So to recap, at the point where the AC source was giving out maximum current in the positive direction, the voltmeter would pick up maximum voltage in the positive direction as well. Now let’s consider maximum current in the opposite direction, so for example at this point in time where the current is negative but maximum. So this time round, current is going this way. And it arrives at this branch point here. Now at this point, it could split either this way or this way. But once again, the orientation of the lower diode does not allow for this. Now the current that is allowed to flow, in other words through this diode, reaches this branching point here.
And once again, it could split left and right, but this diode stops it from doing so. So the current just flows right, once again clockwise through the resistor. How interesting! And now it reaches this branch point, splits along both diodes, and then the current that’s going in both branches meets at this branch point again and continues to flow clockwise yet again through the resistor. So it got messy once again, but to recap. Even the current is flowing counterclockwise this time due to the AC voltage source, we’ve still got a clockwise current through the resistor. Therefore, even though the potential difference from the voltage source is negative, that is flowing counterclockwise, the voltmeter still reading a positive voltage across the resistor.
Now just to remember, we considered a point in time where the current was negative but maximum. And so once again using Ohm’s law, the potential difference is going to be maximum as well. If instead we had considered another point in time where the current was still negative but not maximum, then we’d have a smaller current through the resistor and, therefore, a slightly lower voltage as measured on the voltmeter. And so the behavior in one of these graphs that we’re looking for is that because there’s always a clockwise flow through the resistor, the voltmeter will always read a positive voltage. However, the value of that voltage will indeed go up and down as the current goes up and down due to the potential difference of the source.
In other words then, the graph that we’re looking for is this one here, because the potential difference measured by the voltmeter is always positive but it does go up and down as the value of the current through the resistor increases and decreases. Hence, this graph shows the output voltage as measured by the voltmeter in the circuit diagram. And that’s the interesting thing about this weird part of the circuit. Even though the input current can be in different directions at different points in time, this part of the circuit with the diodes in it ensures that the current through the resistor is always flowing in the same direction. In other words, it’s rectifying the alternating current, ensuring that it’s always positive and no longer flipping between positive and negative.
Okay so now that we’ve discussed this, let’s look at the next part of the question. What kind of circuit is shown in diagram (a)? So in other words, we’re asked to give the name of this kind of circuit. Now to answer this question, we can actually redraw the circuit diagram to make life a little bit easier for ourselves. So let’s start with the voltage source and add some wires either side of the voltage source, some more wire, and then we reach this branch point here. Now instead of drawing that branch off at a diagonal, let’s draw that branch with the diode on it like this. And this diode can be drawn similarly downwards. And then let’s momentarily ignore this branch and this branch, which contain the wires connected to the resistor. Instead let’s continue by drawing this diode over here and this diode on the lower branch here. Now at this branch point then, the current from the two diodes can meet. And then we can finally reconnect back to our voltage source.
So now that we’ve drawn this part of the circuit. We can see that we’ve got two branches with diodes on them, and they’re in parallel with each other. In other words, this branch with the two diodes is connected in parallel with this branch of the two diodes. So that’s an interesting point! And now we can consider the branch with the resistor and the voltmeter on it. Now this piece of wire connected to the resistor meets in between these two diodes on the top branch, in other words over here on our newly drawn circuit diagram. And this piece of wire does the same thing for the diodes in the bottom branch, in other words over here, at which point we can basically draw a resistor between the two orange dots. And of course we need a voltmeter in parallel with the resistor. So essentially what we’ve done is we’ve taken two branches that were in parallel with each other and we’ve connected them at this point and this point with a resistor and a voltmeter. And the resistor and the voltmeter basically act as a bridge between the two parallel branches. And hence, this type of circuit is known as a bridge circuit because the resistor is bridging the two parallel branches of the circuit.