Question Video: Calculating the Uncertainty of Two Resistors Connected in Series Physics • 9th Grade

Two resistors have resistances of 20 ± 0.1 Ω and 80 ± 0.2 Ω. If the two resistors were placed in series, what would the uncertainty of the two resistors together be?

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Video Transcript

Two resistors have a resistances of 20 plus or minus 0.1 ohms and 80 plus or minus 0.2 ohms. If the two resistors were placed in series, what would the uncertainty of the two resistors together be?

Okay, so in this example, we have two resistors. We’ll say that this is our first and then this is our second. And we’re told these two resistors are placed in series with one another. For both, we’re given the value of their resistances. And we see that those resistances include an uncertainty, 0.1 ohms in one case and 0.2 ohms in the other. We can recall that when resistors are placed in series, like they are here, their resistances add together for a total combined resistance value. If these resistance values were stated without uncertainties, it would be straightforward enough to add 20 ohms to 80 ohms to get a total resistance of 100 ohms. But in this case, we do have these uncertainties that we’ll need to consider as well.

The way to do this is to recall our rule for combining uncertainties, specifically when we’re adding two values together. Let’s say that we have one value. We’ll call it 𝑣 sub one. And this is equal to 𝑎 plus or minus the uncertainty in 𝑎. And similarly, we have a second value, 𝑣 two, which is equal to 𝑏 plus or minus the uncertainty in 𝑏. Now, if we were to add 𝑣 one to 𝑣 two, then the way we would do that is we would add 𝑎 and 𝑏 and then, with the uncertainties, add those together as well. We can apply this rule to our particular scenario of adding the values of these two resistors.

If we were to solve for the total resistance, we can call it capital 𝑅, of these two resistors together, then by our rule, that would be equal to 20 plus 80 plus or minus 0.1 plus 0.2 ohms or, in other words, 100 plus or minus 0.3 ohms. Now, it’s not the overall resistance 𝑅 that we want to solve for, but rather the total uncertainty of these two resistors together. In solving for 𝑅, though, we have found that total uncertainty. We see that it’s equal to the sum of the individual uncertainties. That total is 0.3 ohms.

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