How does a short circuit in the parallel portion of a series-parallel circuit affect total resistance?

In a series-parallel circuit, when a short circuit occurs in the parallel section, it creates a pathway of very low resistance. This effectively removes the resistor that was shorted from the circuit (theoretically, it can be considered as having zero resistance). Consequently, the total equivalent resistance for the parallel portion of the circuit decreases significantly.

In a parallel circuit, the total resistance is computed using the formula for equivalent resistance, where multiple resistances combine inversely. The presence of a short circuit reduces the overall resistance because the equation reflects a much lower resistance value in series with other resistances in the circuit. Therefore, the total resistance of the overall circuit decreases because the now minimal resistance of the shorted path dominates the calculation.

This effect can lead to increased current flow through the circuit due to the lower resistance, which can be a point of failure if the other components are not designed to handle the increased current. Thus, the correct understanding is that the occurrence of a short circuit in the parallel portion will result in a decrease in total resistance in the series-parallel circuit.