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Asked by jhajuhi19 | 09 Dec, 2021, 10:00: AM

Expert Answer

Equivalent resistance R of two resistances R₁ and R₂ that are connected in parallel is given as

begin mathsize 14px style 1 over R space equals space 1 over R subscript 1 space plus space 1 over R subscript 2 end style

........................... (1)

begin mathsize 14px style 1 over R space equals space 1 fourth space plus space 1 third space equals space 7 over 12 end style

from above , we get equivalent resistance R = ( 12/7 ) Ω = 1.714 Ω

Uncertaintity in equivalent resistance R is determined by differentiating above relation as ,

begin mathsize 14px style fraction numerator increment R over denominator R squared end fraction space equals space fraction numerator increment R subscript 1 over denominator R subscript 1 superscript 2 end fraction space plus space fraction numerator increment R subscript 2 over denominator R subscript 2 superscript 2 end fraction end style

begin mathsize 14px style increment R space equals space open parentheses fraction numerator R squared over denominator R subscript 1 superscript 2 end fraction close parentheses space increment R subscript 1 space plus space space open parentheses fraction numerator R squared over denominator R subscript 2 superscript 2 end fraction close parentheses space increment R subscript 2 space end style

begin mathsize 14px style increment R space equals space open parentheses fraction numerator 12 over denominator 7 cross times 4 end fraction close parentheses squared space cross times space 0.03 space space plus space space open parentheses fraction numerator 12 over denominator 7 cross times 3 end fraction close parentheses squared space cross times space 0.03 space equals space 0.009 end style

Hence equivalent resistance with uncertaintity = 1.714 ± 0.009 Ω

Answered by Thiyagarajan K | 09 Dec, 2021, 02:02: PM

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