Using the colored bands on the two resistors at your table, you determine that t

Question

Using the colored bands on the two resistors at your table, you determine that the two resistances of the resistors are 100 ohms with 10% tolerance and 200 ohms with a 20% tolerance. What would you expect the equivalent resistance of the two resistors to be (including the uncertainty) if they are connected in parallel?
(___ +/- ___) ohms
Please show work and give uncertainty! Using the colored bands on the two resistors at your table, you determine that the two resistances of the resistors are 100 ohms with 10% tolerance and 200 ohms with a 20% tolerance. What would you expect the equivalent resistance of the two resistors to be (including the uncertainty) if they are connected in parallel?
(___ +/- ___) ohms
Please show work and give uncertainty! Using the colored bands on the two resistors at your table, you determine that the two resistances of the resistors are 100 ohms with 10% tolerance and 200 ohms with a 20% tolerance. What would you expect the equivalent resistance of the two resistors to be (including the uncertainty) if they are connected in parallel?
(___ +/- ___) ohms
Please show work and give uncertainty!

Explanation / Answer

If they are connected in parallel,

1/R = 1/R1 + 1/R2

1/R = R1 +R2 / R1R2

R = ( R1 R2) / (R1 + R2)

R = (100 x 200) / (100 + 200) = 66.67 Ohm

For uncertainty:

R1 + R2 replaced by R'

R' = 300 Ohm +_ 50 Ohm

R = R1 R2 / R'

R1 = 100 +_ 10

R2 = 200+_ 40

deltaR /R =sqrt[ (deltaR1 / R1)^2 + (deltaR2 /R2)^2 + (deltaR' / R)^2 ]'

deltaR / 66.67 = sqrt[(10/100)^2 + (40/200)^2 + (50/300)^2 ]

deltaR = 18.60

So R = 66.67 +_ 18.60 Ohm

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