The circuit is so artificial and abstract there's no telling what a cap would be good for. Mostly caps directly on the supply are there to act as "bulk caps", stabilizing the voltage coming from the supply.

@Lundin My line of thinking was that by adding a big capacitor parallel to the DC voltage source , any noise current due to the thermal noise voltage of the resistors wont flow inside the voltage source which may damage it.

In that case you really need to specify what the voltage source is and why it would be vulnerable to such.