The diagram shows a circuit consisting of a cell and two resistors connected in series. If the total resistance of the circuit is 20 ohms, what is the value of 𝑅?
So this question shows us a circuit diagram in which we have two resistors connected in series. This means that they’re connected one after the other along the same loop. The right-hand resistor has a resistance of seven ohms. Meanwhile, the left-hand resistor is labeled with a resistance of 𝑅. We are asked to work out the value of 𝑅 given that the total resistance of the circuit is 20 ohms.
This total resistance of the circuit is equal to the resistance of both of these two resistors together. So let’s recall what happens when we have two resistors connected in series. To do this, we’ll consider two general resistors, one with a resistance of 𝑅 one, the other, a resistance of 𝑅 two. When the two resistors 𝑅 one and 𝑅 two are connected in series, the total resistance of both of them together, which we’ve labeled as 𝑅 subscript 𝑇, is equal to 𝑅 one plus 𝑅 two. In other words, whenever we have two resistors connected in series, their total resistance is equal to the sum of the individual resistances.
So let’s apply this knowledge to the circuit from the question. We’re told that the total resistance is 20 ohms. And because this value is the resistance of these two resistors connected in series, then we know that this 20 ohms must be equal to the resistance 𝑅 plus the resistance of seven ohms. This leads us to this equation here, which we can use to find the value of 𝑅.
We want to make 𝑅 the subject of the equation. So let’s subtract seven ohms from each side. On the left-hand side, we have 20 ohms minus seven ohms, which gives us 13 ohms. On the right-hand side, we have 𝑅 plus seven ohms minus seven ohms, which is simply equal to 𝑅. And so we have found our answer to the question that the value of 𝑅 is equal to 13 ohms.