What happens to the total resistance in a circuit when one of three parallel pathways is blocked?

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When one of three parallel pathways in a circuit is blocked, the total resistance of the circuit increases. In a parallel configuration, the total resistance is determined by the reciprocal of the sum of the reciprocals of the individual resistances. The formula for the total resistance in parallel is given by:

1/R_total = 1/R1 + 1/R2 + 1/R3

When one pathway is blocked (effectively removing one of the parallel resistors), the total resistance is recalculated using only the remaining pathways. Since adding more pathways (resistors) in parallel decreases the total resistance, removing one will have the opposite effect, thereby causing the total resistance to increase. This increase happens because there is less path for the current to flow through, leading to a higher overall resistance in the circuit.

So, the correct answer is that the total resistance will increase when one of three parallel pathways is blocked.