How do errors in voltage and power relate?

1 Answer
George C.
Feb 26, 2017

I am not sure what you meant to ask, but here's an example that may help...

Explanation:

Suppose you have a circuit with known resistance #R# and apply a voltage #V# to it. The resulting current through the circuit is #I = V/R# and the power dissipated is #VI = V^2/R#.

So the power dissipated is proportional to the square of the voltage.

If you have a #5%# error in measuring the voltage #V#, then what is the error in the calculated power?

Approximately #2xx5% = 10%#

In general, for small values of #epsilon# we have:

#(1+epsilon)^n ~~ 1+n epsilon#

So when raising to the #2#nd power, the error is roughly doubled.

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