Video Transcript
The diagram shows a circuit containing several diodes and resistors. All of the resistors are connected in parallel with the cell. Through which resistors, if any, is the current nonzero?
In our diagram, we see a cell connected in parallel with three resistors 𝑅 one, 𝑅 two, and 𝑅 three. In addition, our circuit has four diodes here, here, here, and here. With each of our resistors in a separate parallel branch of the circuit, charge potentially flows through all three of them. We want to figure out though in which cases this is actually true, through which resistors, if any, is the current nonzero.
To begin figuring this out, let’s notice that in our cell the positive terminal is towards the bottom and the negative terminal is towards the top. We know that conventional current points from positive to negative. Therefore, we can model charge as leaving the positive terminal of the cell and moving in this direction around the circuit. When the charge reaches this first junction point, it can potentially turn upward, pass through the diode, and then on through resistor 𝑅 one.
Let’s recall now what a diode does in an electrical circuit. In such a circuit, a diode functions as a valve, or a one-way switch. It allows the flow of charge in one direction, in the direction indicated by what we could think of as an arrowhead here, while at the same time preventing the flow of charge in the opposite direction. Looking at the diode in this first branch of our parallel circuit, we see that the arrowhead points downward. That means that charge can flow through the diode from top to bottom but not from bottom to top. And indeed from bottom to top is exactly how our conventional current would pass through the diode, if it could.
This diode then blocks the flow of charge in this first branch of our parallel circuit. No charge reaches resistor 𝑅 one, and so the current in this resistor is zero. Since current can’t travel in this branch, all of the current from the cell will continue to move around the circuit until it reaches this junction point. Once again, we want to know if this moving charge can turn up and then pass on through resistor 𝑅 two. However, we see that we once again have a diode which only allows charge flow from top to bottom as it’s oriented. Any electric charge moving from bottom to top would be blocked by this diode. Therefore, moving charge cannot enter this second branch in our parallel circuit. And so the resistor 𝑅 two also has zero current in it.
All of the current in the circuit then will follow this path here. Notice that this diode is oriented so that it allows the flow of charge from bottom to top. Therefore, electric charge can flow through the diode in this direction and then pass through resistor 𝑅 three. However, notice what happens next. The charge encounters this diode. We see from the direction of the triangle, which we could think of as an arrowhead, that this diode only permits the flow of charge from left to right. That means it blocks charge from moving right to left. Since the moving charge in this branch also can’t complete the circuit, we know that actually no current exists anywhere in this third loop.
Overall in our circuit diagram, we don’t have a closed circuit. Current can’t exist anywhere in the circuit, and this tells us what the answer to our question will be. Of our three resistors, 𝑅 one, 𝑅 two, and 𝑅 three, none of them have a nonzero current.
