GATE 2025 EE – Question 31
The maximum percentage error in the equivalent resistance of two parallel-connected resistors of 100 Ω and 900 Ω with each having a maximum 5% error is __________ % (round off to nearest integer value).
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Correct answer: 5
Explanation
$R_{eq}=\dfrac{R_1R_2}{R_1+R_2}=90\ \Omega$. Its relative sensitivity to each resistor is $\dfrac{dR_{eq}}{R_{eq}}=\dfrac{R_2}{R_1+R_2}\dfrac{dR_1}{R_1}+\dfrac{R_1}{R_1+R_2}\dfrac{dR_2}{R_2}=0.9(5\%)+0.1(5\%)=5\%$.