How does the total current relate to the individual currents in a circuit of parallel resistors?
Why In a parallel circuit every branch sees the same voltage, and each branch draws its own current given by I = V/R. Kirchhoff's current law says charge cannot pile up at a node, so whatever flows into the junction must flow out: the source current is the arithmetic sum of all the branch currents. Adding another branch gives the current one more path, so the total current goes up while the total resistance goes down.
Watch out The idea that total current decreases as branches are added gets it backward; it is the total resistance that decreases. Averaging branch currents would violate conservation of charge, and summing reciprocals of voltage drops is a garbled version of the parallel resistance formula.
Parallel = more paths = more current. Currents add in parallel, voltages add in series.