GATE EE 2017 Set 2 — Question 8
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Electrical & Electronic Measurements → Measurement Principles → Error Analysis
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Question
Two resistors with nominal resistance values and have additive uncertainties and , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance is
Correct answer
(A) ± √(((∂ R)/(∂ R₁) Δ R₁)² + ((∂ R)/(∂ R₂) Δ R₂)²)
Solution
According to the law of propagation of errors, for a function , the standard deviation of the error (uncertainty) in is given by the root-sum-square of the individual uncertainties weighted by their sensitivity coefficients:For two resistors and , this becomes:
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