Two resistors with nominal resistance values R 1 and R 2 have additive uncertainties ΔR 1 and ΔR 2 , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

Correct Answer is : ±(∂R∂R1∆R1)2+(∂R∂R2∆R2)2

\pm \sqrt{ (\frac{\partialR}{\partialR_{1}}∆ R_{1}) ^{2} + (\frac{\partialR}{\partialR_{2}}∆ R_{2}) ^{2}}

\pm \sqrt{ (\frac{\partialR}{\partialR_{2}}∆ R_{1}) ^{2} + (\frac{\partialR}{\partialR_{1}}∆ R_{2}) ^{2}}

\pm \sqrt{ (\frac{\partialR}{\partialR_{1}}) ^{2}∆ R_{2} + (\frac{\partialR}{\partialR_{2}}) ^{2}∆ R_{1}}

\pm \sqrt{ (\frac{\partialR}{\partialR_{1}}) ^{2}∆ R_{1} + (\frac{\partialR}{\partialR_{2}}) ^{2}∆ R_{2}}

GATE Electrical Engineering (EE) 2017 Shift 2 Solved Paper

Question : 18 of 65

Marks: +1, -0

Two resistors with nominal resistance values R₁ and R₂ have additive uncertainties ΔR₁ and ΔR₂, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

$± √{ (\;{∂R}/{∂R_{1}}∆ R_{1}) ^{2} + (\;{∂R}/{∂R_{2}}∆ R_{2}) ^{2}}$
$± √{ (\;{∂R}/{∂R_{2}}∆ R_{1}) ^{2} + (\;{∂R}/{∂R_{1}}∆ R_{2}) ^{2}}$
$± √{ (\;{∂R}/{∂R_{1}}) ^{2}∆ R_{2} + (\;{∂R}/{∂R_{2}}) ^{2}∆ R_{1}}$
$± √{ (\;{∂R}/{∂R_{1}}) ^{2}∆ R_{1} + (\;{∂R}/{∂R_{2}}) ^{2}∆ R_{2}}$

Validate

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