What is the relationship between total resistance and branch currents in a parallel circuit?

The relationship stated pertains to the fundamental laws governing parallel circuits. In a parallel circuit, the total current flowing into the circuit is divided among the different branches. Each branch carries a portion of the total current, which can be calculated using Ohm's Law and the individual resistances of the branches.

When the branches are connected in parallel, the voltage across each branch remains the same, while the current can vary based on the resistance of each branch. Consequently, because the total current entering the parallel portion of the circuit is the sum of the currents through each branch, it is mathematically impossible for the individual branch currents to exceed the total current supplied by the source.

This means that the total current equals the sum of the branch currents, ensuring that the combined branch currents will always be equal to or less than the total current. This principle is crucial in circuit analysis, especially when designing and troubleshooting electrical systems. Thus, the statement that branch currents can never exceed total current accurately reflects the behavior of current distribution in parallel circuits.