Question Video: Finding the Potential Difference across Components in Series

A student sets up the circuit shown in the diagram. She uses a voltmeter to measure the potential difference across 𝑅₁ and finds it to be 4 V. She then uses a voltmeter to measure the potential difference across 𝑅₂ and finds it to be 10 V. What is the potential difference across both resistors together?

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Video Transcript

A student sets up the circuit shown in the diagram. She uses a voltmeter to measure the potential difference across 𝑅 one and finds it to be four volts. She then uses a voltmeter to measure the potential difference across 𝑅 two and finds it to be 10 volts. What is the potential difference across both resistors together?

Okay, so in this circuit, we could see that first of all we’ve got a cell. So that’s an EMF source. And that’s causing a current 𝐼 to move this way counterclockwise around the circuit. Next, we can see that we’ve got two resistors, 𝑅 one and 𝑅 two, placed in series within this circuit. And we’ve got voltmeters 𝑉 one and 𝑉 two in parallel with each one of these resistors. These voltmeters are being used to separately measure the potential difference across each one of the resistors.

Now, we’ve been told that the student finds the potential difference across 𝑅 one to be four volts. And across 𝑅 two, it’s 10 volts. In other words, the reading on 𝑉 one is four volts. And the reading on 𝑉 two is 10 volts. We’ve been asked to find the potential difference across both resistors together.

Well, to answer this, we need to recall that components placed in series will share the total potential difference across them. In other words, if the total potential difference across the two resistors is let’s say 𝑉, then some of that potential difference will be dropped across the first resistor. And the rest of it will be dropped across the second resistor. In other words, what we’re saying is that the total potential difference across both resistors is simply total the sum of the potential difference across the first resistor and the potential difference across the second resistor.

If there were more resistors added in series, so, for example, if there was an 𝑅 three placed here, then we would have to add the potential difference across these three, assuming of course that 𝑉 was the total potential difference across all three of the resistors now.

However, that’s not the case. And we don’t need to worry about this. In this circuit, we only have two resistors. They’re being placed in series. And we’re saying that the total potential difference across both together is 𝑉. And we can say that 𝑉 is equal to four volts, that’s the potential difference across the first resistor, plus 10 volts, that’s the potential difference across the second resistor. Or, in other words, 𝑉 is equal to 14 volts.

And hence, we found the final answer to our question. The potential difference across both resistors together is 14 volts.

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