Calculating RSS Uncertainty of 2 Resistors in Series & Parallel

In summary, Jed has two resistors, R1 = 120.0 ± 0.30 Ω and R2 = 65.6 ± 0.15 Ω. The RSS uncertainty for the resistance of these two resistors in series is 125.4 Ω and the RSS uncertainty for the resistance of these two resistors in parallel is 33.4 ± 0.39 Ω. The relative uncertainty for the two cases is 275.3%.
  • #1
nate13
1
0
I'm having problems with this:

Jed has two resistors, R1 = 120.0 ± 0.30 Ω and R2 = 65.6 ± 0.15 Ω. Give all answers to 2 significant digits.
(a) Calculate the RSS uncertainty for the resistance of these two resistors in series.
(b) Calculate the RSS uncertainty for the resistance of these two resistors in parallel.
(c) Compare the relative uncertainty (in percent) for the two cases.


This is what I've tried so far for part a, but i know it's wrong:
2jdgtqx.jpg


Any help is appreciated!
 
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  • #2
a) RSS Uncertainty for resistance of two resistors in series = sqrt(120.0 + 0.30^2 + 65.6 + 0.15^2) = 125.4 Ωb) RSS Uncertainty for the resistance of these two resistors in parallel = 1/(1/120.0 + 1/65.6) ± sqrt((0.30/120.0)^2 + (0.15/65.6)^2) = 33.4 ± 0.39 Ωc) Relative uncertainty for the two cases = (125.4 - 33.4)/33.4 x 100% = 275.3%
 

Related to Calculating RSS Uncertainty of 2 Resistors in Series & Parallel

What is the formula for calculating RSS uncertainty of 2 resistors in series?

The formula for calculating the RSS (Root Sum Square) uncertainty of two resistors in series is:
uRSS = √(uR12 + uR22)
Where uR1 and uR2 are the individual uncertainties of the resistors.

What is the formula for calculating RSS uncertainty of 2 resistors in parallel?

The formula for calculating the RSS (Root Sum Square) uncertainty of two resistors in parallel is:
uRSS = Req √( (uR1 / R1)2 + (uR2 / R2)2 )
Where Req is the equivalent resistance of the parallel resistors, and uR1 and uR2 are the individual uncertainties of the resistors.

How do you calculate the equivalent resistance of 2 resistors in parallel?

The formula for calculating the equivalent resistance of two resistors in parallel is:
Req = (R1 * R2) / (R1 + R2)
Where R1 and R2 are the values of the individual resistors.

What is the significance of calculating RSS uncertainty for resistors in series and parallel?

Calculating the RSS uncertainty for resistors in series and parallel helps to determine the overall uncertainty of the circuit. This is important for accurately measuring and predicting the behavior of the circuit and ensuring the accuracy of experimental results.

Can the RSS uncertainty of a circuit be reduced by using more resistors in series or parallel?

Yes, using more resistors in series or parallel can reduce the overall RSS uncertainty of a circuit. This is because the individual uncertainties of the resistors will be divided by a larger number, resulting in a smaller overall uncertainty. However, it is important to note that adding more resistors can also increase the complexity and cost of the circuit.

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