Kirchhoff's Second Law


The algebraic sum of the potential differences in a circuit loop must be zero.  Potential rises are + while potential drops are -.

Kirchhoff's second law when officially stated (see insert at the right) sounds more complicated than it actually is.  Generally speaking, it says, around any loop in a circuit, the voltage rises must equal the voltage drops.  Another way of thinking about this is to consider that whatever energy a charge starts with in a circuit loop, it must end up losing all that energy by the time it gets to the end.  Or we could say that by the time a charge makes it to the end of a circuit, it must have given all its energy to do work.

The diagrams below represent several possible circuits or loops within a circuit.

1 source, 1 resistor, 1 loop (4k)

This is a simple circuit showing the potential differences across the source and the resistor.  According to Kirchhoff's 2nd law the sum of the potential differences will be zero.

1 source, 2 resistors, 1 loop with potentials shown(2k) This diagram shows the potentials in the little circles and then shows the potential differences off to the side.  Notice that the potential difference is actually the difference between one potential and another.  Moving from a low potential to a high potential is considered a potential rise or positive potential difference.  Moving from a high potential to a lower potential is considered a potential drop or negative potential difference.
1 source, 2 resistor, 1 loop (4k) This animation shows the same circuit as above but only looks at the potential differences as you go around the loop.  Again, Kirchhoff's 2nd law says the sum of the potential differences has to be zero.
1 source,  2 resistors, 2 loops (10k) This animation shows a multiple loop circuit.  Once again, the sum of the potential differences as you go around the loop is zero.  This is true no matter which loop you look at.

1999 Science Joy Wagon