How does the equivalent resistance of a parallel circuit compare to the branch with the lowest resistance value?

In a parallel circuit, the total or equivalent resistance is always less than the smallest resistance value among the branches. This occurs because the branches provide additional paths for current to flow, effectively reducing the overall resistance of the circuit.

When resistances are connected in parallel, the current can divide among the branches, and the total current is the sum of the currents through each branch. The equivalent resistance can be calculated using the formula for parallel resistances, which results in a value that approaches zero as more branches with lower resistance are added. Thus, the presence of any resistor in parallel lowers the total resistance below that of the smallest resistor present in the circuit.

This principle is fundamental in circuit analysis and essential for understanding how different configurations affect overall resistance in electrical circuits.