Propagation of uncertainty problem

[libelec]

Homework Statement

Find the equivalent resistance viewed by A and B and its equivalent uncertainty:
http://img707.imageshack.us/img707/5040/dadadadaz.png

R₁ = 10ohm, 5% tolerance.
R₂ = 2ohm, 1% tolerance.
R₃ = 5ohm, 5% tolerance.
R₄ = 15ohm, 1% tolerance.

The Attempt at a Solution

The R_eq = (1/R₁ + 1/R₂)^-1 + (1/R₃ + 1/R₄)^-1 = 65/12ohm = 5,41ohm.

Now, for the uncertainty, I separated the problem in two: first, find R_A (10/6ohm), the equivalent resistance of the first two resistors and R_B (15/4ohm), the equivalent resistance of the second two resistors, and then add them.

I was given a formula for propagation of uncertainty for parallel resistors and for series resistors, based in the formula for a function f(x₁, x₂,..., x_k): $$\mu$$_f = $$\sum$$|(x_k/f)*(f'_xk)|*$$\mu$$_xk:

For two parallel resistors: $$\mu$$ = (R₂/(R₁+R₂))*$$\mu$$_R1 + (R₁/(R₁+R₂))*$$\mu$$_R2

For two series resistors: $$\mu$$ = (R₁/(R₁+R₂))*$$\mu$$_R1 + (R₂/(R₁+R₂))*$$\mu$$_R2

If I do the calculus, I get that the total uncertainty is 3,28%: the uncertainty of A is 2/(10+2)*0.05 + 10/(10+2)*0.01 = 1/60, and the one of B is 15/(15+5)*0.05 + 5/(15+5)*0.01 = 1/25. Then the total uncertainty is (10/6)/(65/12)*1/60 + (15/4)/(65/12)*1/25 = 0.0328 = 3.28%.

But the answer given by the problem says it has to be 8.7%.

I'd like to know if I'm using the formulas right, or if I should be doing something with the uncertainties instead of that.

Thanks.

 

[libelec]

Anybody?

 

[ehild]

I got the same result as you.

ehild

 

[libelec]

Then the answer I was given is wrong? Or is there another method I could have used to reach that answer?

Thanks.

 

[ehild]

Sometimes wrong answers are given. Your calculation was correct but a bit overcomplicated.

Unless the function is a product or fractions of its variables, calculate with absolute uncertainties instead of relative ones.

$$\Delta f = \Sigma (|\frac{\partial f }{\partial x_i}|\Delta x_i)$$

Divide the absolute error with the value of f if relative uncertainty is needed.

ehild