Inverting Gain Is a Resistor Ratio - Electronic Circuits V & VI: Front-End Conditioning and Op-Amp Feedback Step by Step

This inverting-gain-is-resistor-ratio lesson treats the inverting node as an ideal virtual ground, so input current through one resistor must be supplied through the feedback resistor. The 2 V over 2 ohm input current and 6 ohm feedback resistor give -6 V exactly only for the stated ideal op-amp model. Real op-amps add finite gain, offset, bias current, bandwidth limits, slew rate, rail limits, resistor tolerances, and measurement uncertainty.

An inverting op-amp output follows from the input current through feedback resistance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The input resistor sets the current

The input is 2 volts across 2 ohms, so the input-resistor current is 1 ampere.

I = \frac{2\ \text{V}}{2\ \text{ohm}} = 1\ \text{A}

The output moves negative through the feedback resistor

The same current through 6 ohms requires -6 volts at the output.

V_{\text{out}} = -\left(1\ \text{A}\right)\cdot 6\ \text{ohm} = -6\ \text{V}