How are the currents through?

Question

how are the currents through the individual resistors related to the current supplied by the battery?

Answer 1

Kirchoff's law. The current out of the battery is equal to the sum of the currents in the loads.

That is if the resistors are in parallel.

In series, the same current flows in each resistor and that is the current the battery delivers.

Answer 2

they are related by :

Kirchhoff's current law (KCL)

The algebraic sum of the currents at a junction in a closed circuit is zero.

and

Kirchhoff's voltage law (KVL)

The algebraic sum of the potential differences in any loop including those associated with emfs and those of resistive elements must be equal to zero.