Question Video: Finding the Total Resistance of Components in Series Physics • Third Year of Secondary School

Video Transcript

A student sets up the circuit shown in the diagram. If the value of 𝑅 is three ohms, what is the current through the circuit?

Okay, so in this question, we have a circuit diagram. And we can see from the diagram that we have a cell in this circuit which provides a potential difference of 10 volts. This cell is connected to two resistors in series. One of these resistors has a resistance of seven ohms. The other one is labeled as 𝑅. We’re told in the question that the value of 𝑅 is three ohms. So, let’s go ahead and add this to our diagram. The question asks us to work out the current through the circuit.

We can recall that potential difference, resistance, and current are related through Ohm’s law. Specifically, Ohm’s law says that potential difference 𝑉 is equal to current 𝐼 multiplied by resistance 𝑅. In this equation, if 𝑉 is the potential difference provided by the cell, then 𝑅 is the total resistance of the two resistors. In fact, to distinguish it from the resistor labeled 𝑅 in the circuit diagram, we’ll label this total resistance as 𝑅 subscript 𝑇. So, let’s work out the value of 𝑅 subscript 𝑇 for the circuit shown in the diagram.

To see how we find the total resistance of two resistors connected in series, we’ll consider two general resistors with resistances 𝑅 one and 𝑅 two. The total resistance of two resistors in series is equal to the sum of the individual resistances. So, for the resistors 𝑅 one and 𝑅 two, the total resistance 𝑅 subscript 𝑇 is equal to 𝑅 one plus 𝑅 two. In the circuit diagram from the question, we have one resistor with a resistance of three ohms and another with a resistance of seven ohms. The total resistance of these two resistors 𝑅 subscript 𝑇 will therefore be equal to three ohms plus seven ohms. Adding together three ohms and seven ohms, we get that this total resistance 𝑅 subscript 𝑇 is equal to 10 ohms.

The potential difference across these two resistors is equal to the potential difference provided by the cell, which is 10 volts. So, we have that 𝑉 is equal to 10 volts. Looking at our Ohm’s law equation, we see that we know values for the potential difference 𝑉 and the resistance 𝑅 subscript 𝑇. We want to find the value of the current 𝐼. So, we need to rearrange this equation to make 𝐼 the subject. To do this, we’ll take our Ohm’s law equation and divide both sides by the resistance 𝑅 subscript 𝑇. On the right-hand side of the equation, we have an 𝑅 subscript 𝑇 in the numerator, which cancels with the one in the denominator. And so, we have that 𝑉 divided by 𝑅 subscript 𝑇 is equal to 𝐼. We can also write this equation the other way around to say that current 𝐼 is equal to potential difference 𝑉 divided by resistance 𝑅 subscript 𝑇.

The final step is to take our values for 𝑉 and 𝑅 subscript 𝑇 and to substitute them into this equation to calculate the current 𝐼 through the circuit. Substituting these values gives us that 𝐼 is equal to 10 volts — that’s our value of 𝑉 — divided by 10 ohms, our value for 𝑅 subscript 𝑇. Evaluating this expression gives us that 𝐼 is equal to one amp. And this value of 𝐼 is the current through the circuit, which is what we were asked to find.

And so, our answer to the question is that the current through the circuit is equal to one amp.