Understanding the Concept:
The concept of a virtual short is an analytical tool used when studying operational amplifiers operating in a stable negative feedback configuration. The fundamental transfer characteristic equation of an operational amplifier is:
\[
V_{\text{out}} = A_{vd} (V_+ - V_-)
\]
Where:
• \(A_{vd}\) is the open-loop differential voltage gain of the op-amp.
• \(V_+\) is the voltage potential present at the non-inverting input terminal.
• \(V_-\) is the voltage potential present at the inverting input terminal.
For an ideal operational amplifier, the open-loop differential gain (\(A_{vd}\)) approaches infinity (\(\infty\)).
Step 1: Deriving the input voltage relationship under negative feedback.
Rearranging the basic transfer formula to look at the input differential voltage gives:
\[
(V_+ - V_-) = \frac{V_{\text{out}}}{A_{vd}}
\]
When negative feedback is applied, the output voltage \(V_{\text{out}}\) is stable and finite. Taking the limit as the ideal open-loop gain \(A_{vd}\) approaches infinity yields:
\[
\lim_{A_{vd} \to \infty} (V_+ - V_-) = \frac{V_{\text{out}}}{\infty} = 0
\]
This mathematical result shows that:
\[
V_+ \approx V_- \quad \Rightarrow \quad V_+ - V_- \approx 0
\]
Step 2: Clarifying the term 'virtual' short circuit.
This condition indicates that the operational amplifier adjusts its output via the negative feedback path to maintain the voltage difference between its input terminals at nearly zero. It is called a virtual short because while the voltages are held at the same potential, no physical current flows between the two terminals due to the op-amp's near-infinite input impedance. This aligns with Option (D).