Video: Deducing Which Light-Emitting Diodes in a Circuit Are Lit

The diagram shows a circuit containing several diodes and LEDs. How many of the LEDs in the circuit are lit?

10:34

Video Transcript

The diagram shows a circuit containing several diodes and LEDs. How many of the LEDs in the circuit are lit?

Okay, so in this question, we’ve been given a diagram of a rather complicated electrical circuit containing various different electrical components. For example, in this circuit, we can see that we’ve got a cell, a resistor, some diodes, specifically one, two, three, four diodes in our circuit. And we’ve also got some light-emitting diodes or LEDs in our circuit. We’ve got one, two, three, four of those as well.

Now in order to go about working out what’s happening in this circuit, let’s first start by recalling that a diode is a circuit component that only allows current to pass through it in one direction. In other words, if we’re discussing conventional current, which is the flow of positive charge. Then the diode only allows conventional current to pass through it in the direction of the arrow found in its circuit symbol. This means that conventional current can flow in this direction through the diode, but not in the opposite direction.

And actually, a light-emitting diode or LED works in a similar fashion. It only allows conventional current to pass through it in the direction of the arrow found in its circuits symbol. But the rather special thing about an LED is that when there is a current passing through it, it also emits light, which is why it’s called a light-emitting diode.

So to answer the question, “How many of the LEDs in the circuit are lit?” We need to try and work out how many of the LEDs have a current through them. To work this out, we’re going to need to remember two different rules. The first rule is that an electric current only flows from a higher potential to a lower potential and not the other way round. So what do we mean by this?

Well, in this case, we’ve got a cell here. And the cell provides energy to all the charge carriers moving through the circuit. If we’re talking about conventional current, then it’s a flow of positive charges from the positive terminal of the cell, the larger terminal. Going around the circuit and coming all the way back to the negative terminal, the smaller of the two. And the cell is providing these charges with energy. This energy is lost throughout the circuit whenever the current passes through some circuit component. And we traditionally think about this energy being lost as a voltage drop.

So, for example, we may say that the battery provides 24 volts of potential or, in other words, a voltage of 24 volts to the current, leaving the positive terminal. And therefore, we can think of all the current in this part of the circuit as being at 24 volts until it reaches this resistor here. Because once it passes through the resistor, it loses some of that voltage. That voltage is said to be dropped across our resistor.

And so we could say, for example, that 10 volts are dropped across the resistor. This means that the current now moves through the circuit with the remaining 14 volts. And it stays at 14 volts until it reaches another circuit component. Whether that’s this diode here or whether it goes this way and reaches this diode here. And so one way to think about potential and specifically higher and lower potential is to imagine that. Every piece of wire that touches any other piece of wire without going through a circuit component is at exactly the same potential.

In other words, if our cell is indeed a 24-volt cell, then this entire piece of wire until it gets to the resistor is at 24 volts. And then if 10 volts really are dropped across the resistor. Then every piece of wire after the resistor before touching any other circuit component can be thought of as being at 14 volts. And a higher potential basically is a higher number. 24 volts is a higher potential than 14 volts. And this means that a current cannot pass through the resistor in this direction. Because the higher potential is here and the lower potential is here. It must go this way.

Now of course, the values we’ve used of 24 volts and 14 volts here are just arbitrary. They’re made up. But the idea still holds. And so we’ll have to use rule number one momentarily, that current only flows from a higher potential to a lower potential. We can even imagine this as a river of water only flowing downhill. It never goes back up the hill. It’s moving from a higher gravitational potential to a lower gravitational potential. And every part of the hill at exactly the same height is said to be at exactly the same gravitational potential. Just like how every wire that touches every other wire without going through a circuit component is said to be of the same electrical potential.

So now that we’ve discussed rule number one, we’ll talk about rule number two that we’ll need to understand this particular circuit. As we’ve already seen, this particular circuit is full of diodes and light-emitting diodes. And so, for us, rule number two is going to be that current only flows in the direction permitted by a diode. And that includes LEDs.

So now that we know all of this, let’s imagine current flow from the positive terminal of the cell around the circuit and trying to get to the negative terminal. And once again, we’re talking about conventional current. So that’s a flow of positive charges.

Now when the current reaches the resistor, it passes through. And some voltage is dropped across that resistor, as we’ve seen already. This means that the current in the pink part of the circuit is at a lower potential than the current in the orange part of the circuit. And interestingly, when current reaches this branching point, it’s got two directions it can travel in. Firstly, it could go straight downwards or it could go towards the right.

Let’s talk about it going downwards first. If it was to go straight down, then it would have to travel in this direction, against the direction allowed by the diode. Because it only allows current to pass through this way. And so because the diode forbids current from flowing downward, there’ll be no current in this branch. And this is where we’ve made use of rule number two, which means all of the current now flows in this direction through the diode. And this current is allowed to flow in that direction because the directionality of the diode allows it to do so.

However, flowing through the diode results in some sort of voltage drop across it. And so we can say that the potential of this wire, which we’re now labeling in orange once again, is lower than this pink wire. And of course, that pink region includes the wire the current has traveled through earlier. So the entirety of this orange region is at the same potential. And that potential is lower than the pink potential.

So anyway, the current does pass through the diode because it’s allowed to do so. And at that point, it reaches this junction here. Now at that junction, the current could split into this direction and this direction. However, if we look ahead at this branch and specifically the orientation of the diode, we can see that the diode only allows current to pass through in the other direction. And therefore, there is no current allowed to pass through in this branch. Which means all of the current passes through this branch and specifically through the light-emitting diode. And it passes in this direction.

Now because there is a current passing through this light-emitting diode, this diode is going to be lit up. Because, as we mentioned earlier, a current allowed to pass through a light-emitting diode causes it to light up. And additionally, we can realize that because current has passed through a circuit component, there’s been some voltage dropped across that circuit component. And therefore, the potential of the current in this part of the wire is low again. And we’re gonna draw this bit as a dotted orange line to show that this is at a different potential compared to, say, this orange potential or this pink potential or even this orange potential. This is just to prevent confusion.

But essentially, we’re once again linking up all of the bits of wire that touch the wire through which the current is passing without passing through another circuit component. Because these are all at the same potential. Anyway, so the current continues to flow around our circuit and reaches this branch point here.

Now at this point, it could split off into this direction and this direction. But we see that if it was to pass through in this direction, then it would have to go through the light-emitting diode present at that point in the circuit in the wrong direction. This is forbidden once again by rule two. And so there is no current flowing through that part of the circuit. Instead, all of it flows along the lower branch and arrives at this diode here.

Now that diode does allow current to pass through in that direction because the orientation of the diode is correct. And we once again recall that there’s a voltage drop across that diode. So the potential of the wire after the diode is different. We use pink once again to label all of the wires with that potential. Note that we’ve colored this potential pink again. But it is not the same as this potential, which we’ve also colored pink.

But anyway, so all other wires touching this part of the pink potential without going through a circuit component are all of these bits of wire. Anyway, so the current flows through this diode. And it arrives now at this junction here. Now current could split off into this direction and this direction. And if it was to go in this direction, we can see that the diode is in the correct orientation to allow it to do so.

However, remember that this wire on the other side of the diode that we’re currently considering is at the same potential as this wire here. And current has already flowed through that wire earlier on. Which means if we use our gravitational analogy of the hill again, that would be like a bit of the river flowing downstream and then flowing back up again to a height where the river had already been before. In this particular case, we’re talking about this height here. Because even though the river itself hasn’t flowed at this point before, it has passed that height in a different part of the hill.

And in the same way, current cannot flow in this direction because the potential of this wire is higher than this potential. And we know this because the current has already been at that potential before. So there is no current in this direction, which means that there is no current flowing through this diode. Even though the diode would permit this just solely based on the direction in which current is allowed to flow through a diode.

This means that, at the branch point, all of the current must go down this way. And then it arrives at this branch point here, at which point current could split in this direction and this direction. But of course, it can’t go this way because of the LED. The LED only allows current to pass through it in this direction. And so all of the current must now flow this way. It does pass through this LED because, once again, the orientation is correct. And the LED causes a potential drop. And as the current passes through the LED, it causes the LED to light up. So current continues to flow in this direction.

Now let’s use a pink dotted line to link up all of the pieces of wire at the same potential. Or, in other words, that connect to all other pieces of wire without passing through a circuit component. So that’s this bit of wire and all of this bit of wire, which will eventually take us back all the way around to the negative terminal of the cell. So all of those wires are at exactly the same potential. And specifically, that potential is lower than this pink potential here because we’ve just come from a wire at that pink potential.

Anyway, so current flows this way through our circuit and arrives at this branch point. At this point, it could go this way or upwards. And if it goes this way, then we can see that the LED would indeed allow it. But once again, we’ve got all of these dotted orange wires, which are all at the same potential. And we’ve already had current flowing through a wire at that potential before. This means that the dotted orange potential is higher than the dotted pink potential. And so current cannot flow in this direction because it can’t go from a lower potential to a higher potential, once again as told by rule one. This means that all of the current flows this way. And at this point, we’ve come all the way round to the negative terminal of our cell.

So we’ve navigated the entire circuit. And we’ve worked out which way the current flows all the way through it. And on the way, we’ve seen that this LED and this LED have currents passing through it. Which means that those two LEDs are lit. So the answer to the question “How many of the LEDs in the circuit are lit?” is two. And that is our final answer.

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