Chapter 12
Kirchhoff’s Rules, Terminal Voltage
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12
Kirchhoff’s Rules, Terminal Voltage
There are two circuit-analysis laws that are so simple that you may consider them “statements of
the obvious” and yet so powerful as to facilitate the analysis of circuits of great complexity.
The
laws are known as Kirchhoff’s Laws.
The first one, known both as “Kirchhoff’s Voltage Law”
and “The Loop Rule” states that, starting on a conductor
1
, if you drag the tip of your finger
around any loop in the circuit back to the original conductor, the sum of the voltage changes
experienced by your fingertip will be zero.
(To avoid electrocution, please think of the finger
dragging in an actual circuit as a thought experiment.)
Kirchhoff’s Voltage Law (a.k.a. the Loop Rule)
To convey the idea behind Kirchhoff’s Voltage Law, I provide an analogy.
Imagine that you are
exploring a six-story mansion that has 20 staircases.
Suppose that you start out on the first floor.
As you wander around the mansion, you sometimes go up stairs and sometimes go down stairs.
Each time you go up stairs, you experience a positive change in your elevation.
Each time you
go down stairs, you experience a negative change in your elevation.
No matter how convoluted
the path of your explorations might be, if you again find yourself on the first floor of the
mansion, you can rest assured that the algebraic sum of all your elevation changes is zero.
To relate the analogy to a circuit, it is best to view the circuit as a bunch of conductors connected
by circuit elements (rather than the other way around as we usually view a circuit).
Each
conductor in the circuit is at a different value of electric potential (just as each floor in the
mansion is at a different value of elevation).
You start with your fingertip on a particular
conductor in the circuit, analogous to starting on a particular floor of the mansion.
The
conductor is at a particular potential.
You probably don’t know the value of that potential any
more than you know the elevation that the first floor of the mansion is above sea level.
You
don’t need that information.
Now, as you drag your finger around the loop, as long as you stay
on the same conductor, your fingertip will stay at the same potential.
But, as you drag your
fingertip from that conductor, through a circuit element, to the next conductor on your path, the
potential of your fingertip will change by an amount equal to the voltage across the circuit
element (the potential difference between the two conductors).
This is analogous to climbing or
descending a flight of stairs and experiencing a change in elevation equal to the elevation
difference between the two floors.
If you drag your fingertip around the circuit in a loop, back to the original conductor, your finger