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If R is the total resistance of two resistors connected in parallel with resistances R_1 and R_2, then?

If R is the total resistance of two resistors connected in parallel with resistances R_1 and R_2, then R = (R_1*R_2)/(R_1+R_2). If R_1 is measured to be 17 ohms with a possible percentage error of 3 percent while R_2 is measured to be 33 ohms with a possible percentage error of 5 percent, use differentials to estimate the maximum percentage error in the calculation of R.

I cant seem to calculate R

2 Answers

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  • s
    Lv 7
    7 years ago
    Favorite Answer

    R1 = 17 ohms, R2 = 33 ohms

    R {nominal} = 17 || 33 = 11.22 ohms

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    R1 = 17 ± 3% , therefore R1 = 17 + 3% for maximum and R1 = 17 - 3% for minimum

    17 * 0.03 = 0.51 ohms ; 17.51 ohms {maximum} 16.49 ohms {minimum}

    R2 = 33 ± 5% therefore R2 = 33 + 5% for maximum and R1 = 33 - 5% for minimum

    33 * 0.05 = 1.65 ohms ; 34.65 ohms {maximum} 31.35 ohms {minimum}

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    17.51 ohms {maximum} || 34.65 ohms {maximum}

    Rmax = 11.6319 ohms

    deviation = 11.6319 - 11.22 ohms = +0.4119 ohms

    % deviation = +3.6714%

    17.51 ohms {maximum} || 31.35 ohms {minimum}

    Rmid1 = 11.2349 ohms

    deviation = 11.2349 - 11.22 ohms = +0.0149 ohms

    % deviation = 0.1330%

    16.49 ohms {minimum} || 34.65 ohms {maximum}

    Rmid2 = 11.1728 ohms

    deviation = 11.1728 - 11.22 ohms = -0.0472 ohms

    % deviation = -0.4204%

    16.49 ohms {minimum} || 31.35 ohms {minimum}

    Rmin = 10.8061 ohms

    deviation = 10.8061 - 11.22 ohms = -0.4139 ohms

    % deviation = -3.6894%

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    Therefore worst case deviation from the nominal value, is when both resistors are at their minimum tolerance.

    Source(s): vast engineering experience.
  • Anonymous
    7 years ago

    let

    X = R_1 , Y=R_2

    1/R = 1/X + 1/Y , differentiate ---> dR/R^2 = dX/X^2 + dY/Y^2

    X=17 , Y=33 --->R=11.22

    and with dX/X=3% , dY/Y = 5%

    --->dR/R = 3.68% , this is maximum error

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