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Homework Statement
We are told that resistor 1 has a resistance of 4700Ω ± 5% and resistor 2 has a resistance of 6800Ω ± 5% and the equivalent series and parallel resistances are to be calculated with an estimate of uncertainty.
Homework Equations
RSeries = R1 + R2
RParallel = R1 × R2 / R1 + R2
Uncertainties can simply be added if their measured numbers are added or subtracted.
The formula we were given for multiplying or dividing uncertainty is the following:
If z = x ⋅ y or z = x / y
Then
Δz=z(√(Δx/x)2+(Δy/y)2) (The square root covers everything in the equation except for z)
The Attempt at a Solution
I believe that I am doing the math correctly, but my the method doesn't really appear to correspond to anything else I have seen.
I have done the following:
RSeries = 4700 + 6800 =11500Ω
Uncertainty = 235 + 340 = 575Ω (That's just 5% of each number)
I feel that my method might be going wrong here:
R1 × R2 = 4700 × 6800 = 31,960,000
Uncertainty ≅ 2,259,913.273 (Using the uncertainty multiplication/division formula)
The bottom half of the parallel equation has already been calculated.
To get the equivalent resistance and uncertainty, I used the multiplication/division formula again.
RParallel = 31,960,000 / 11500 ≅ 2,779Ω
Uncertainty = 2779(√(2,259,913.273 / 31,960,000 )2 + (575 / 11500)2)
Which gives ~241Ω.
Is 2779 ± 241Ω a correct and acceptable way to display this answer or have I done something wrong here? Any feedback would be appreciated.