In the discussed circuit, closing the switch results in an increase in the ammeter's reading due to the addition of parallel resistance, which allows more current to flow. The voltage remains constant from the source, but the terminal voltage decreases because of the internal resistance of the voltage source, which is affected by the increased current. The conversation emphasizes the importance of understanding physical concepts alongside calculations to avoid errors in reasoning. Additionally, the discussion touches on the distinction between total power and wasted power, clarifying that wasted power refers to energy lost as heat in the internal resistance of the battery. Overall, the participants engage in a detailed exploration of circuit behavior and the implications of resistance and voltage changes.