Golden Rules of the Op-Amp explained in less than 5 minutes

This video lays down the op-amp basics you need for exam and design work by explaining the two golden rules and when they actually apply. First, we state the relationship that is always true for any operational amplifier: V_out = A·(V_+ − V_-). From this, the first golden rule follows under the ideal model: no current enters the inputs, so I_+ ≈ I_- ≈ 0. The second golden rule—V_+ ≈ V_-—is not a universal law; it holds only in negative-feedback configurations while the amplifier remains in its linear region. In that ideal, high-gain limit (A → ∞), the node equality creates a virtual short between the inputs, and when V_+ is tied to ground the inverting node becomes a virtual ground, which is the backbone of inverting amplifier analysis and KCL-based derivations.

We then show how to handle the non-ideal case with finite open-loop gain A (or A_OL). The exact equation V_out = A·(V_+ − V_-) still holds, but the input voltages are no longer equal. Rearranging gives V_- = V_+ − V_out/A, which quantifies the input error. If V_+ = 0, then V_- = −V_out/A, explaining why the “virtual ground” is only approximately at 0 V when A is large but finite. You’ll see how these relationships propagate through common inverting and non-inverting topologies, how loop gain determines accuracy, and why the golden rules fail in positive feedback or saturation. By the end, you’ll know exactly when to invoke virtual short or virtual ground, how to correct ideal results for finite A, and how to use KCL/KVL with V_out = A·(V_+ − V_-) to move cleanly between ideal and non-ideal predictions.