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20 June, 07:39

2 Resistors of resistance, R = (100 + - 3) Ohm, R2 = (200+-4) Ohm are connected in Parallel and Series.

Find the absolute error and % error in the measurement of equivalent resistance are in each combinations I. e Series and Parallel ... ?

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  1. 20 June, 10:10
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    According to what I've learnt, in any expression of multiplication or division, the percentage errors of each term are added up to find the equivalent percentage error. That is, if

    y = ABC

    y = ABC then % error in y = % error in A + % error in B + % error in C

    For the above problem, let Rs denote series combination. Then Rs = 300±7 ohm.

    Let Rp denote parallel combination.

    ∴ Rp = R1 R2 / R1 + R2 = R1 R2 / Rs

    Ignoring errors, we get Rp = 200/3 = 66.67 ohm

    % error in R1 = 3, % error in R2 = 2, % error in Rs = 7/3

    Hence, % error in Rp = 3+2 + 7/3 = 22/3

    So, error in Rp will be 22/3 % of 200/3, which is approximately 4.89.

    Hence, I got Rp = 66.67±4.89 ohm.

    However, the book used the formula described and proved here and arrived at the answer Rp = 66.67±1.8 ohm.
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