Inverting Gain Is a Resistor Ratio - Electronic Circuits VI: Op-Amp Feedback and Exact Gain Networks Step by Step

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}