Kirchoff’s Laws for Circuits

Kirchoff’s Laws

This past week in lab we built series and parallel circuits.  A variety of circuits were made.  Between a test on Monday and a blizzard on Friday, there wasn’t much time this week.  If you want to watch a iTunes download I recorded in 2010 of the derivations of the resistance equations from Kirchoff’s Laws click here.

But some background information on where those resistance equations come from, as the text and workbook are rather vague on the topic.

The theory of circuits can be explained with what we call Kirchoff’s Circuit Laws.   The Wikipedia page explanation of Kirchoff’s Laws tends to be needlessly complex.  But Wikipedia does lead us to a nice analysis us Kirchoff’s original writing in a text by Kalil T. Swain Oldham. Oldham mentioned on p52 the discovery of the Laws.  He also goes into detail on pp 142-144.

Kirchoff’s Current Law

This rule basically says that the current into a junction is equal to the current out of a junction.  If 5 electrons go into a wire, 5 electrons must come out.  If 5 gallons of water go into a pipe, 5 gallons must come out.

You can find a more indepth explanation at hyperphysics.

Kirchoff’s Voltage Law

This rule says the the change in voltage around a closed loop is equal to zero.  I like to call this the roller coaster rule.  Suppose you get on a roller coaster on the ground.  The roller coaster might climb up a hill (a battery), come down a hill (a resistor), go up another hill (a second battery) and come back down (another resistor).  When you go to get off the ride, hopefully the roller coaster has brought you back down to the ground.  If it hasn’t, when you get off the roller coaster you might have a big fall!

The same can be said for circuits.  A battery causes a voltage rise in the circuit.  There is a voltage drop over a resistor. And there will be some small but finite voltage drop over the wires themselves.  How does the voltage know to get back down to zero?  You might say that the electric field tells it to behave this way.  What is interesting with the parallel circuit is that no matter what path you take, the voltage drop is the same.  And with the series circuit, the voltage drops for both resistors adds up to the voltage rise from the battery.  In the below diagram, B is for battery, and 0 is for ground.

You can find a more indepth explanation at hyperphysics.