In a negative-feedback op-amp circuit, the voltage gain is set by the feedback network—the ratio of the resistors in the feedback path—rather than by what the load does at the output. The op-amp adjusts its output so that the voltage at the inverting input matches the input voltage, enforcing a fixed relationship between input and output determined by that resistor ratio. The load simply draws current from the output; as long as the load is within the amplifier’s ability to drive (no excessive current, no saturation or output impedance effects beyond design limits), the feedback keeps the same output voltage ratio, so the gain stays constant. If the load were to demand more current than the device can supply, you’d see a change due to output limitations, but within design limits the gain remains the same.

Voltage comparators are designed to decide which of two voltages is higher and to produce an output that reflects that decision. This makes them act as level detectors: they monitor a signal against a fixed reference and flip their output when the signal crosses that threshold. When the input surpasses the reference, the output switches to a high level; when it falls short, the output goes low. This threshold-crossing behavior is what you use to sense that a particular voltage level has been reached or exceeded. They’re not meant to amplify signals like amplifiers, not meant to generate repeating waveforms like oscillators, and not meant to accumulate input over time like integrators.

To null or adjust the output offset, you want the two input terminals to sit at the same potential so any remaining output is due only to the offset voltage inside the amplifier. Tying both inputs to the circuit common provides that common reference point, making the input differential effectively zero. With both inputs at the same level, you can use offset-trim provisions (if present) to dial the output back to zero. If you connect an input to the power supply, the inputs aren’t forced to be equal and the amplifier may drive to a rail or behave unpredictably. Connecting to the output node would disturb the feedback behavior and won’t set the inputs equal. Grounding both inputs works if ground is the same as the circuit’s common reference, but the intended and reliable practice is to use the circuit common, which is the designated reference for offset adjustment.

In a multiple-feedback active filter, the passive network around the op-amp sets the locations of the poles of the transfer function. Those pole locations determine the center frequency and how sharply the filter responds, i.e., the Q factor. So choosing the resistor and capacitor values primarily tunes where the center frequency lies and how selective the filter is. The overall gain at the center frequency comes mainly from the amplifier configuration and feedback resistor ratios, not from the pole positions themselves. Noise performance, while influenced by resistor values and the op-amp, is not what these component choices primarily establish.