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Homework Help: Help please with Differentials

  1. Mar 25, 2008 #1
    Hello,

    I'm having trouble with this maths question and was wondering if someone could help me?? The question asks:


    The electrical resistance R of a wire is given by

    k / r^2 where k = constant, r = radius of wire.

    Use differentials to estimate the percentage error in the measured value of r if we want the percentage error in R to be within +/- 3%.


    I'm really not sure if this is the right approach... please help me...

    Using the method of linear approx. i have...
    ΔR = R(r + Δr) - R(r)
    ~ (dR(r) / dr) * ( Δr )

    I know...
    R = k / r^2
    dR/dr = -2*k*( r^-3 )

    and therefore...
    ΔR = -2*k*( r^-3 ) * ( Δr )

    So i'm thinking to increase R by 3% i need...
    ΔR / R(r) = 0.03

    but after substituting everything in i get Δr = 0.03??

    please i really need help!!
     
  2. jcsd
  3. Mar 25, 2008 #2

    Shooting Star

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    R = k/r^2 =>
    dR = -(2k/r^3)dr =>
    dR/R = -2(dr/r).

    Now put dR/R = 6/100 to find the corresponding dr/r.
     
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