Operational amplifier basics — Inverting amplifier input impedance (Zin): In a standard inverting op-amp configuration using an ideal op-amp, with input resistor Ri feeding the inverting (−) input and a feedback resistor Rf from output to the inverting node (the noninverting (+) input at ground), the small-signal input impedance seen by the source is approximately equal to which element?

Introduction:
In the classic inverting amplifier, understanding input impedance helps you size the driving source and limit noise and loading. With an ideal operational amplifier, the virtual short between inputs and the very high input resistance at the op-amp terminals simplify the small-signal input impedance seen by the source.

Given Data / Assumptions:

• Ideal op-amp (infinite open-loop gain, infinite input resistance, zero input bias currents)
• Inverting topology: source → Ri → inverting node; Rf from output to inverting node
• Noninverting input tied to ground (0 V)
• Linear (unsaturated) operation with negative feedback

Concept / Approach:

In linear operation, the inverting node is held near 0 V (virtual ground). The source therefore “sees” a resistor to virtual ground equal to Ri. Because the op-amp input draws negligible current, essentially all source current flows through Ri, not into the op-amp pin.

Step-by-Step Solution:

Verification / Alternative check:

More exact analysis with finite open-loop gain still yields Zin ≈ Ri for high gains; deviations are small for typical op-amps in closed-loop use.

Why Other Options Are Wrong:

• Rf + Ri or Rf − Ri: Rf is in the feedback path, not in series with the source at small-signal input.
• ∞ (infinite): That describes the op-amp input pin, not the network seen by the source.
• Depends primarily on op-amp open-loop gain: In practice Zin is dominated by Ri in closed loop.

Common Pitfalls:

• Confusing op-amp input pin resistance with network input impedance.
• Forgetting the virtual-ground assumption only holds in linear, unsaturated operation.

Final Answer:

Ri