Error propagation when you take the inverse?

[homestar]

Say something is a value +/- .05. What happens when you take the inverse of the value? For example, 30 V +/- .05 V. 1/V...what would the error be?

 

[mathman]

This is a math question. 1/(x+y)=1/(x(1+y/x)).=.(1/x)(1-y/x)=1/x-y/x².

The assumption is|y|<<|x|, .=. means approx =

I'll let you do the arithmetic.

 

[pam]

When you take the inverse, use % error. That is the same for the inverse as for the original.

 

[|\|a|\|]

Sorry, I have the same qns but i don't get what both of you are saying, elaborate with example? thanks

 

[jtbell]

In the original question, the error in V is 0.05 V or (0.05/30)*100% = 0.1667%.

1/V = 0.0333 V^{-1}. The error in this is also 0.1667%, or about 0.0000556 V^{-1}.

 

[Andy Resnick]

The uncertainty in any function of one variable is \delta y = \left|\frac{dy}{dx}\right| \delta x. If y = x^n (in your case n = -1), then \frac{\delta y}{|y|} = |n| \frac{\delta x}{|x|}. For your case, the error is unchanged.

Taylor's book "An introduction to error analysis" is well worth reading.