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 20% tolerance and 330 ohms with a 10% tolerance. What would you expect the equivalent resistance of the two resistors to be (including the uncertainty) if they are connected in parallel?

Answer 1

R₁ = 100 +/- 20 ohm

R₂ = 330 +/- 33 ohm

Parallel resistence= (R₁xR₂)/(R₁+R₂)

Parallel resistence= (100 * 330) /(100+330) = 76.74

Parallel resist. error= ( R₁² dB + R₂² dA ) / (R₁+ R₂)²
where R1=100.0 +/- 20 ohm and R2=330.0 +/- 33 ohm

error=(100² x 20+330² x 33)/(100 + 330)²= 20.517 ohm
therefore R_eqv = 76.74 +/- 20.517 ohm