Question

A resistor of 10 kΩ with the tolerance of 5% is connected in parallel with 5 kΩ resistors of 10% tolerance. What is the tolerance limit for a parallel network?

(a) 9%

(b) 12.4%

(c) 8.33%

(d) 7.87%

This question was posed to me during an online exam.

My query is from Advanced Problems on Error Analysis in Electrical Instruments in chapter Measurement of Resistance of Electrical Measurements

Answer 1

Right option is (c) 8.33%

Easy explanation: Here, R1 and R2 are in parallel.

Then, \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}\)

Or, R = \(\frac{50}{15}\) kΩ

∴\( \frac{△R}{R} = \frac{△R_1}{R_1^2} + \frac{△R_2}{R_2^2}\)

And △R1 = 0.5×10^3,   △R2 = 0.5×10^3

∴\( \frac{△R}{R} = \frac{10 × 10^3}{3 × 10 × 10^3} × \frac{0.5 × 10^3}{10 × 10^3} + \frac{10}{3} × \frac{10^3}{5 × 10^3} × \frac{0.5 × 10^3}{5 × 10^3}\)

= \( \frac{0.5}{30} + \frac{1}{15} = \frac{2.5}{30}\) = 8.33%.