


Current is the same through each resistor; in essence that is the definition of "series,"
that one end of each resistor is hooked together and nothing else at that point.
The potential difference supplied by the battery is shared by the three resistors. How the voltage is shared 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:




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:

Resistors R_{1} and R_{2} are in series; one end of each is connected, with nothing else at junction. Same current flows through each resistor. 


Resistors R_{2} and R_{3} are in parallel; ends of both are directly connected to each other, with nothing between. Same voltage difference across each resistor. 
(or in series either.) 
"http://www.physics.udel.edu/~watson/phys208/clas0220.html"
Last updated Feb. 21, 1998.
Copyright George Watson, Univ. of Delaware, 1997.