How do errors in voltage and power relate?

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How do errors in voltage and power relate?

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Answer 1 · 2017-02-26T13:21:29

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 $R$ $R$ and apply a voltage $V$ $V$ to it. The resulting current through the circuit is $I = \frac{V}{R}$ $I = V/R$ and the power dissipated is $V I = \frac{V^{2}}{R}$ $VI = V^2/R$ .

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

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

Approximately $2 \times 5 % = 10 %$ $2xx5% = 10%$

In general, for small values of $ε$ $epsilon$ we have:

${(1 + ε)}^{n} \approx 1 + n ε$ $(1+epsilon)^n ~~ 1+n epsilon$

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

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How do errors in voltage and power relate?

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