An open in a parallel branch causes a circuit's total resistance to what?

In a parallel circuit, multiple paths are available for current to flow. When an open occurs in one of these parallel branches, it disrupts the current flow in that specific branch, but it does not affect the current flow in the other branches. The total resistance of a parallel circuit is calculated using the reciprocal of the sum of the reciprocals of the individual resistances in each branch.

When a branch becomes open, only the resistances of the remaining branches contribute to the total resistance. As a result, the overall resistance increases because the total current is divided among fewer paths. This leads to a higher total resistance compared to when all branches are intact. If two or more paths are available and one goes open, the remaining paths have to carry the current, thus increasing the resistance faced by the source powering the circuit.

The scenario of an infinite resistance applies when there are no connected paths left for current to flow, but that would not be the case here since other branches are still available. Conversely, a resistance of zero would only occur if there were a direct short circuit that bypassed all resistance, which is not the situation when just one branch opens. Therefore, in this case, the correct result is that the total resistance increases due to the loss