The circuit in the diagram consists of two resistors in series. What is the total resistance of the two resistors?
So in this question, we’re told that we have two resistors in series. That means connected one after the other along the same loop of wire. The resistance of each of the resistors is labeled for us in the diagram. And we’re asked to work out the total resistance of both of these resistors together.
So let’s recall how we add resistances in series. We’ll consider two general resistors connected in series. We’ll suppose that the first resistor has a resistance of 𝑅 one and the second resistor has a resistance of 𝑅 two. If we label the total resistance of these two resistors together as 𝑅 subscript 𝑇, then we have that 𝑅 subscript 𝑇 is equal to 𝑅 one plus 𝑅 two. In other words, whenever we have two resistors connected together in series, the total resistance of those two resistors together is equal to the sum of the individual resistances.
In the circuit diagram from this question, we have one resistor with a resistance of seven ohms and a second resistor with a resistance of five ohms. We can find the total resistance of these two resistors together, which we’ll label as 𝑅 subscript 𝑇 by adding the two resistances. So that’s seven ohms, the resistance of the left-hand resistor, plus five ohms, the resistance of the right-hand resistor. Adding together seven ohms plus five ohms gives a result of 12 ohms. And so our answer to the question is that the total resistance of the two resistors is equal to 12 ohms.