How Does Error in Radius Affect Resistance Calculations?

[caelestis]

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!

 

[Shooting Star]

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%.

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.