Yes, they both can add a load to a circuit.
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For DC circuits, an alebraic sum is required. For AC circuits, a phasor sum is required.
The opposition of current flow is measured in ohms. For DC circuits it is resistance and for AC circuits it is impedance.
In any rectifiers circuits the purpose is to get a DC voltage by giving AC voltage as input.by connecting capacitors parallally in the circuit it is possible to get pure DC output.capacitor filter only eliminates the ac quantities remainimg in the output waveforms.so that finally we get pure DC for further aplications in electronics circuits.
We don't know much about the circuit these capacitors are in, but they are coupling capacitors. Coupling capacitors isolate DC between stages or circuits, and they couple AC between those circuits or stages. Only the signal gets in and goes out. The DC the stage operates on is isolated from stage to stage.
Kirchoff's Voltage and Current Laws apply to all AC circuits as well as DC circuits. Other laws, such as Ohm's law and Norton and Thevanin equivalents apply equally as well. The complicating factor is that, at AC, current and voltage are not usually in phase with each other, unless it is a simple resistive circuit. That makes the math harder, but it does not make it invalid or impossible.