Uncertainty

Two resistors of resistances 120 ohms and 500 ohms are connected in parallel. The percentage uncertainty in the value of resistance of each resistor is 10%.

What is the correct value of the total resistance and the percentage uncertainty?

Reply 1

old_survivor

6

For resistors a and b in parallel is it given: 1/Rtotal = 1/Ra + 1/Rb

so Rtotal = 1/(1/120 + 1/500) = 3000/31 = 96.774... = 97 to 2.s.f

For uncertainty in different operations:

when adding/subtracting: add the absolute uncertainties
when multiplying/dividing: add the percentage uncertainties

so we were dividing so 10% + 10% = 20%

97ohms +or- 20%

Reply 2

vaishnoraj

OP

6

Original post by old_survivor

For resistors a and b in parallel is it given: 1/Rtotal = 1/Ra + 1/Rb

so Rtotal = 1/(1/120 + 1/500) = 3000/31 = 96.774... = 97 to 2.s.f

For uncertainty in different operations:

when adding/subtracting: add the absolute uncertainties
when multiplying/dividing: add the percentage uncertainties

so we were dividing so 10% + 10% = 20%

97ohms +or- 20%

In the markscheme, the answer is 97 ohms + or - 10%

(Source: Question 8 from AS Level Physics A - H156/01 Breadth in Physics - 23 May 2017 - Morning)

Original post by vaishnoraj

Two resistors of resistances 120 ohms and 500 ohms are connected in parallel. The percentage uncertainty in the value of resistance of each resistor is 10%.

What is the correct value of the total resistance and the percentage uncertainty?

Original post by vaishnoraj

In the markscheme, the answer is 97 ohms + or - 10%

(Source: Question 8 from AS Level Physics A - H156/01 Breadth in Physics - 23 May 2017 - Morning)

To find the answer as 97 Ω ± 10%, do the following.

Find the maximum resistance R_max and minimum resistance R_min.

The error is

error = \dfrac{R_{\max} - R_{\min}}{2}

The ‘correct” resistance can be calculated using 97 Ω and 120 Ω.

Reply 4

vaishnoraj

OP

6

Sorry. I am not understanding.

Original post by vaishnoraj

Sorry. I am not understanding.

old_survivor had already shown how to obtain the effective resistance 97 Ω, which is I meant by “correct” resistance. I made a typo in post #4.

“The ‘correct” resistance can be calculated using 500 Ω and 120 Ω.”

Let assume R₁ = 120 ± 10% and R₂ = 500 ± 10%.

To obtain the maximum resistance, you use

R₁ = 120 + 10% and R₂ = 500 + 10%