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Either input pin can be given a positive or negative voltage with respect to the other input pin and also operates the unchanging DC difference between the two inputs (\$f=0\text{ Hz}\$). Then how is the process used by the opamp to amplify AC and DC signals? I mean the path, route or the internal circuitry behavior.

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    \$\begingroup\$ The question is not clear. If we disregard frequency response of a circuit, AC can be regarded as a bunch of momentary DC values. \$\endgroup\$
    – Eugene Sh.
    Sep 29, 2021 at 17:36
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    \$\begingroup\$ They follow the law of superposition. \$\endgroup\$
    – user16324
    Sep 29, 2021 at 17:40
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    \$\begingroup\$ @Eugene Sh. And correspondingly DC can be considered to be AC at at arbitrarily low frequency \$\endgroup\$
    – Frog
    Sep 29, 2021 at 18:47
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    \$\begingroup\$ Comparators are designed to work in an open loop config and amplify the difference of voltage between the two inputs. Their output transitions from +VDD to -VEE. Other opamp configs use feedback to get a small stable gain and perform a function. \$\endgroup\$
    – Syed
    Oct 1, 2021 at 5:01

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enter image description here

Figure 1. Internals of the ancient 741 op-amp. Source: Wikipedia.

From the internal schematic of the (woefully out-of-date) 741 op-amp you can see that there is a DC path from the inputs (blue box) to the outputs (cyan box) so there is no problem with controlling the output from a DC input.

It should also be clear that the output can source current from the \$ V_{S+} \$ rail via Q14 or sink current to the \$ V_{S-} \$ rail via Q20. Nearly all (there are probably exceptions) op-amps will have a similar push-pull arrangement on the output.

Either input pin can be given a positive or negative voltage with respect to the other input pin, so I think the op-amp can work with AC signals.

DC can also be either polarity.

But also operates the unchanging DC difference between the two inputs (f = 0 Hz). Then how is the process used by the op-amp to amplify AC and DC signals?

Op-amps when used as amplifiers are configured so that negative feedback minimises the difference between the two inputs. As you progress in your studies of op-amps you will learn that they have very high "open-loop" gain and this is "tamed" with feedback to give precise control of the gain. The result is that the difference between the two inputs is very small (μV to mV).

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