The GATE Grind

GATE 2014 EE (EE2) – Question 57

Electrical and Electronic Measurements · Oscilloscopes, Error analysis · 2 marks · Multiple choice

Parallel resistors R₁ = 300 Ω and R₂ = 200 Ω each have tolerance 1%. Find equivalent-resistance tolerance.

  1. 0.5%
  2. 1%
  3. 1.2%
  4. 2%

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 1%

Explanation

For R=R1R2/(R1+R2),the first-order relative change is(R2/(R1+R2))δR1/R1+(R1/(R1+R2))δR2/R2. The positive weights sum to1,so worst-case equal1%errors yield **1%,B**. Indeed scaling both resistors by1.01scales their parallel combination exactly by1.01.