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I am sure you will get some feedback after reformulating your question (more precise).
My first answer is: The question makes no sense since in dc analysis all capacitors play no role at all.
Or do you mean time (transient) analysis?
I have drawn a simplr RC circuit .If we analyise it we get a output at Vout but with delay.Now these type of circuits are used extensively in circuit.So my question is what are general applications of these circuits
Angy, the answer is simple: When you speak of "delay" you refer to a specific time scale.
For example, when there is a switch-on at t=0 (you should include such a switch in the diagram) the capacitor is loaded according to the basic exponential law.
But please realize, that this is not a dc analysis but a transient analysis.
And - as you probably know - in ac circuits the shown RC combination is a first order lowpass.
Let's say you have multiple supply voltages going into a microcontroller. You may want to ensure all supply voltages are brought up before bringing the MCU out of reset. One simple way of doing this is to put an RC circuit on the RESET signal that is fed from one of the supply voltages. When that supply voltage is brought up, the microcontroller will not come out of reset according to the RC time constant. This will give you enough time for all the other power supplies to come up.