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Question

# Two resistors R1 and R2 are connected in series. The value of resistance are R1=100.0±0.1Ω,R2=50±0.03Ω If the error in R1orR2 has to be considered as standard deviation then the standard deviation in series equivalent resistance is

A
±0.13Ω
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B
±0.10Ω
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C
±0.20Ω
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D
±0.15Ω
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Solution

## The correct option is B ±0.10Ω When the two resistances are connected in series, the resultant resistance is R=R1+R2 ∂R∂R1=1and∂R∂R2=1 Hence, standard deviation in series is resistance σR=√(∂R∂R1)2σ2R1+(∂R∂R2)2σ2R2 =±√12(0.1)2+(1)2(0.03)2=±0.104Ω

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