Parallel Circuits



The voltage difference is the same across each resistor;
in essence that is the definition of "parallel."
The current through the battery is shared by the three resistors. How the current splits among the three branches is determined by the relative resistance of each resistor.


Combining the two equations via Ohm's law:

The simple equivalent circuit is required to have the same current through the battery, given the same applied voltage:  



Comparison of the equations above yields:
