# How do errors in voltage and power relate?

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 $I = \frac{V}{R}$ and the power dissipated is $V I = {V}^{2} / R$.

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:

${\left(1 + \epsilon\right)}^{n} \approx 1 + n \epsilon$

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