Past exam of the physics 2 paper of the University of Oxford / 2022 / 2

An ideal operational amplifier has infinite input impedance, so neither input draws electric current, and zero output impedance, so its prescribed output voltage is independent of the output electric current within the ideal model. These are the two additional assumptions needed here.

The non-inverting input is grounded, so the finite voltage gain gives $V_{\mathrm{OUT}}=-A{V}^{-}$, or $V^{-}=-V_{\mathrm{OUT}}/A$. Infinite input impedance makes Kirchhoff's current law at the inverting inputSubstitute $V^{-}=-V_{\mathrm{OUT}}/A$ and multiply by $R_1{R}_2$:Hence the inverting operational amplifier hasAs $A\to \infty$, the voltage gain tends to $-R_2/R_1$. Setting $V^{-}=0$ before taking that limit would discard precisely the correction being calculated.