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GATE 2020 IN – Question 35

Measurements · Errors and uncertainty: SI units, standards of R, L, C, voltage, current and frequency, systematic and random errors, uncertainty, accuracy and precision, propagation of errors, linear and weighted regression · 1 mark · Numerical answer

Two 100 Ω resistors of tolerances 3% and 4% are connected in series. Find effective combination tolerance in percent, to one decimal place.

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Correct answer: 2.5 to 2.5 OR 3.5 to 3.5

Explanation

The nominal total is 200 Ω. Worst-case absolute errors add to $3+4=7$ Ω, giving $100(7/200)=3.5\%$. If independent random errors are combined by root-sum-square, the absolute uncertainty is $\sqrt{3^2+4^2}=5$ Ω, or $2.5\%$. The source does not specify the uncertainty convention; the official key accepts exactly 2.5 or 3.5, and both isolated alternatives are preserved.

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