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Plz solve this question using formula ∆Rp/Rp = ∆R1/R1 +∆R2/R2+∆(R1+R2)/(R1+R2)

Asked by jhajuhi19 | 05 Jan, 2021, 08:19: PM

Expert Answer

Relative error for parallel resistance R_p 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, 09:04: PM

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