A battery supplying 12 volts is connected in series with two resistors. The potential difference across the first resistor is four volts. What is the potential difference across the second resistor?
Okay, so in this question, we’ve been told that we’ve got a battery which supplies 12 volts and is connected in series with two resistors. So let’s draw a diagram of that to see exactly what’s going on. So first of all, here’s our battery. Remember, a battery consists of two or more cells. Therefore, we haven’t just drawn one cell, but rather we’ve drawn two.
We could draw more if we wanted to. However, to keep it simple we’ll draw just a two-cell battery. And now that we have our battery, we’ve been told that it’s connected in series with two resistors. So here are the two resistors connected in series. This is the first one, and this is the second one. Now another piece of information that we know is that the battery supplies 12 volts.
And we also know that the potential difference across the first resistor, which we’ll call 𝑉 one, is equal to four volts. Now what we’ve been asked to do is to find out something which we’ll call 𝑉 two, the potential difference across the second resistor. Now since the two resistors are connected in series, the sum of their potential differences is going to equal the voltage supplied by the battery, which is 12 volts.
In other words, 𝑉 one plus 𝑉 two is equal to 12 volts. And we already know that 𝑉 one is four volts. So four volts plus 𝑉 two is equal to 12 volts, at which point we can rearrange to find out the value of 𝑉 two by subtracting four volts from both sides. When we do this, the four volts cancels with the negative four volts on the left-hand side, leaving us with just 𝑉 two on the left and, on the right, we have 12 volts minus four volts, which is eight volts.
Now this expression comes about because the voltage from the battery is shared by components in series. Therefore, if the battery is supplying 12 volts and four volts go to the first resistor and the only other thing in the circuit is the second resistor connected in series, then the second resistor is going to have a potential difference of the remaining eight volts across it. Therefore, at this point, we have our final answer. The potential difference across the second resistor is eight volts.