Valore efficace

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Valore efficace

$\begin{displaymath} i_{C_{rms}}=\sqrt{\frac{1}{N}\sum ^{N}_{k=1}i^{2}_{C}\left( kT_{C}\right) }\end{displaymath}$

Incertezza della radice quadrata di una misura $y$ : $U_{\sqrt{y}}=\left\vert \frac{\partial \sqrt{y}}{\partial y}\right\vert U_{y}=\frac{1}{2\sqrt{y}}U_{y}$

In questo caso $y=\frac{1}{N}\sum ^{N}_{k=1}i^{2}_{C}\left( kT_{C}\right) \Rightarrow U_{i_{C... ... }\frac{1}{2\sqrt{\frac{1}{N}\sum ^{N}_{K=1}i^{2}_{C}\left( kT_{C}\right) }}=$
$=\frac{1}{N}\sum _{k=1}^{N}U_{i^{2}_{C}\left( kT_{C}\right) }\frac{1}{2i_{C_{rms}}}$

Incertezza del quadrato di una misura: $U_{y^{2}}=U_{y}\left\vert y\right\vert +U_{y}\left\vert y\right\vert =2U_{y}\left\vert y\right\vert$

In questo caso $y=i^{2}_{C}\left( kT_{C}\right) \Rightarrow U_{i^{2}_{C}\left( kT_{C}\right) }=2U_{i_{C}\left( kT_{C}\right) }i_{C}\left( kT_{C}\right)$

In definitiva:

$\begin{displaymath} U_{i_{C_{rms}}}=\frac{1}{Ni_{C_{rms}}}\sum ^{N}_{k=1}U_{i_{C}\left( kT_{C}\right) }i_{C}\left( kT_{C}\right) \end{displaymath}$

2001-10-22