The figure shows an electric circuit where all the bulbs are lit. If bulb 𝑋 one went out, which bulb would still be lit? Okay, so this question, we’ve got a circuit, consisting first of all of a cell and then of bulbs 𝑋 one, 𝑋 two, 𝑋 three, and 𝑋 four. We’ve been told in the question that, initially, all the bulbs are lit. But then, bulb 𝑋 one goes out. So this bulb is no longer functioning. That means that a current is no longer flowing through the bulb. So as a result of this, we need to work out whether any of the other bulbs go out and therefore which of the other bulbs still remain lit. So to answer this, let’s think about the current flowing through the circuit, starting at the cell here. Now, let’s specifically think about conventional current, which will flow from the positive terminal of the cell to the negative terminal. This means that the current is going to start here and flow this way. But very quickly, it reaches a junction. Now, at this junction, some of the current would flow this way. And some would go this way. Looking at the branch with the bulb 𝑋 one on it, we’d see that the current flows to the bulb 𝑋 one and then goes round this way through 𝑋 two and then continues to flow anticlockwise, where it arrives at this junction here. And if we look at the branch with the bulb 𝑋 three on it, we can see that the current flows through 𝑋 three and meets that junction as well. Now, at the junction, both current flows merge. And the current flows this way through the circuit now, through the bulb 𝑋 four, still continuing to flow anticlockwise and then meeting the negative terminal of the cell. So that’s what happens initially when all of the bulbs are lit. However, what happens when bulb 𝑋 one is no longer functioning? Well, if the bulb has gone out, we can say that the filament in the bulb, for example, is broken. And therefore, that part of the circuit is broken. This means that no current can flow through the bulb. And therefore, any of the current on this branch is no longer flowing. We can erase all of these current flows, because the broken bulb 𝑋 one essentially acts like an open switch, thus preventing current from flowing through that part of the circuit. However, the fact that the bulb 𝑋 one is broken does not stop the current in this branch. And that continues to flow. Therefore, there still is a current through the bulb 𝑋 three. And we can see that this current also flows through the bulb 𝑋 four, before returning back to the negative terminal of the cell. However, because the bulb 𝑋 one is broken, it does not allow any current to flow through 𝑋 two either. Therefore, 𝑋 two is also not going to be lit.
And so the bulbs which have current flowing through them, that’s bulbs 𝑋 three and 𝑋 four, are going to be the ones that are still lit. And that is our answer to this question.