zakinutuzi

2021-12-17

$\frac{Vs}{Ri}+\frac{{V}_{0}}{Rf}=0$
${V}_{s},Ri,{V}_{0}$ and Rf are just variables for voltage and resistance. After some rearanging, it becomes:
$\frac{{V}_{0}}{{V}_{s}}=-\frac{Rf}{Ri}$
How did the fractions "swap"?

sukljama2

Expert

$\frac{Vs}{Ri}+\frac{{V}_{o}}{Rf}=0$
$\frac{{V}_{o}}{Rf}=-\frac{Vs}{Ri}$
$\frac{{V}_{o}×Ri}{Rf}=-{V}_{s}$
${V}_{o}×Ri=-{V}_{s}×Rf$
$\frac{{V}_{o}×Ri}{{V}_{s}}=-Rf$
$\frac{{V}_{o}}{{V}_{s}}=-\frac{Rf}{Ri}$

intacte87

Expert

$\frac{{V}_{s}}{{R}_{i}}+\frac{{V}_{o}}{{R}_{f}}=0⇒\frac{{V}_{0}}{{R}_{f}}=-\frac{{V}_{s}}{{R}_{i}}$
Now multiplying each side by $\frac{{R}_{f}}{{V}_{s}}$ yields
$\frac{{V}_{o}}{{V}_{s}}=-\frac{{R}_{f}}{{R}_{i}}$

RizerMix

Expert