Question

How do errors in voltage and power relate?

Answer 1

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.