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Plz solve this question using formula ?Rp/Rp = ?R1/R1 +?R2/R2+?(R1+R2)/(R1+R2)
question image
Asked by jhajuhi19 | 05 Jan, 2021, 20:19: PM
answered-by-expert Expert Answer
Relative error for parallel resistance Rp is calculated from the given formula
 
begin mathsize 14px style fraction numerator increment R subscript p over denominator R subscript p end fraction space equals space fraction numerator increment R subscript 1 over denominator R subscript 1 end fraction space plus space fraction numerator increment R subscript 2 over denominator R subscript 2 end fraction space plus space fraction numerator increment left parenthesis space R subscript 1 plus R subscript 2 space right parenthesis over denominator left parenthesis space R subscript 1 plus R subscript 2 space right parenthesis end fraction end style ......................(1)
 
begin mathsize 14px style fraction numerator increment R subscript 1 over denominator R subscript 1 end fraction space equals space.01 space left parenthesis space g i v e n space right parenthesis end style  ....................(2)
begin mathsize 14px style fraction numerator increment R subscript 2 over denominator R subscript 2 end fraction space equals space.02 space left parenthesis space g i v e n space right parenthesis end style .....................(3)
Δ(R1 + R2 ) = ΔR1 + ΔR2 = ( 0.03 + 0.12 ) Ω = 0.15 Ω
 
begin mathsize 14px style fraction numerator increment open parentheses R subscript 1 space plus space R subscript 2 close parentheses over denominator R subscript 1 plus R subscript 2 end fraction space equals space fraction numerator 0.15 over denominator 9 end fraction space equals space 0.0167 end style  .................(4)
By substituting relevant values from eqn.(2) , (3) and (4) , we rewrite eqn.(1) as
 
begin mathsize 14px style fraction numerator increment R subscript p over denominator R subscript p end fraction space equals space 0.01 space plus space 0.02 space plus space 0.0167 space almost equal to 0.047 end style
hence percentage error in parallel resistance = 4.7 %
Answered by Thiyagarajan K | 05 Jan, 2021, 21:04: PM

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