Question

Resistances R1 and R2 have respectively, nominal values of 10Ω and 5Ω and limiting error of ± 5% and ± 10%. The percentage limiting error for the series combination of R1 and R2 is?

(a) 6.67%

(b) 5.5%

(c) 7.77%

(d) 2.8%

I had been asked this question in an international level competition.

This intriguing question comes from Advanced Problems on Error Analysis in Electrical Instruments topic in chapter Measurement of Resistance of Electrical Measurements

Answer 1

The correct option is (a) 6.67%

Easy explanation: R1 = 10 ± 5%

R2 = 5 ± 10%

R1 = 10 ± \( \frac{5}{100}\) × 10 = 10 ± 0.5Ω

R2 = 5 ± \( \frac{5}{100}\) × 5 = 5 ± 0.5Ω

The limiting value of resultant resistance = 15 ± 1

Percentage limiting error of series combination of resistance = \( \frac{1}{15}\) × 100 = 6.67%.