Question

3 You are working in a lab building resistor circuits and you realize the project you have been assigned requires a precise 1% tolerance 17.0? resistor. The closest you can find is a 16.9? resistor. You try contacting your labs supplier to order the resistor only to find out the 16.9? at 1% tolerance is as close as they manufacture. You're supervisor has an excess supply of 10.0? 1% tolerance resistors and instructs you to construct a resistor circuit comparable to the 17.0? resistor. A) Use what you know about combining resistors in series and parallel to construct the 17.0? resistance circuit.

Answer 1

if we consider a circuit where one R1 = 16.9 ohm +- 1% tolerance is in series with 100 R2 = 10 ohm +- 1% toleranceresistors ( which are in parallel to each other)
then

combined resistance is
R = R1 + R2/100
R1 = 16.9 ohm
R2 = 10 ohm
hence R = 17 ohm

now tolerance of R1 = 1%
tolerance of R2 = 1%
tolerance of dR' where R' is parallel combination of toe R2 ressitors is
R' = (1/R2 + 1/R2)^-1 = R2/2
dR'/R' = d(R2)/R2
dR' = (R'/R2)dR2 = dR2/2 = 0.5%
hence

total tolerance of Reff = 1% + 1/100 % = 1.01%
HENCE
THE given combination has resistance of 17 ohm with a tolerance of 1.01% which is comparable to the required tolerance of 1%