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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

RR1=1andRR2=1
Hence, standard deviation in series is resistance

σR=(RR1)2σ2R1+(RR2)2σ2R2

=±12(0.1)2+(1)2(0.03)2=±0.104Ω


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