Inverting Amplifier

Governed by:

$$V_{\text{out}}=V_{\text{in}}\times -\frac{R_f}{R_i}$$

The signal is applied through $R_i$ to $V_{-}$ while $V_{+}=0$

Negative feedback means the op-amp is trying to minimize $V_{+}-V_{-}$, so we can assume $V_{+}=V_{-}$. Ends up causing a current balance since the op-amp is trying to make $V_{-}=0V$ and no current goes into input tereminals.

$$\begin{array}{r}{I}_{in}=\frac{V_{in}-0}{R_i}=\frac{0-V_{out}}{R_f}\\ \therefore \frac{V_{out}}{V_{in}}=-\frac{R_f}{R_i}=A\left[\frac{V}{V}\right]\end{array}$$