Electric Circuits and Kirchhoff's Laws
From xkcd.com
Electrons possess electric potential energy that can be transformed into heat, light, and motion. For such transformations to occur, we need to connect a source of electric potential energy to one or more components by means of a circuit, which is a path for electric current.
Any component or device in a circuit
that transforms electric potential energy into some other form of energy, causing an electric potential drop, is called a load.
Electric current can go through a circuit only if the circuit provides a complete path. Any break in the circuit will cause the electric current to cease. The circuit is then said to be an open circuit. If, by chance, two wires in a circuit touch, so that charge can pass from one wire to the other and return to the negative terminal of the source without passing through the load, the circuit is said to be a short circuit, or, simply, a “short.”
When drawing out circuits on paper, there are certain symbols that must be used. A list of these symbols is found on page 641 of your textbook.
There are two main types of circuits that we'll investigate:
Series Circuits
Parallel Circuits
There are two main types of circuits that we'll investigate:
Series Circuits
ONE PATH
In this type of connection, the charges have only one path to follow through the circuit, and as a result each charge must go through each load in turn: every charge that goes through a series circuit goes through each load in the circuit before returning to the source. There are two main types of circuits that we'll investigate:
Parallel Circuits
In this type of connection, the charges can move along several paths through the circuit and, as a result, pass through any one of the several loads in the circuit. Every charge that goes through the parallel circuit goes through only one of the circuit’s loads before returning to the source.
To understand how simple series and parallel circuits operate, we need to answer two basic questions:
1. When charges have several loads to pass through, what governs the amount of electric potential energy they will lose at each load?
2. When charges may follow several possible paths, what governs the number of charges that will take each path?
German physicist Gustav Robert Kirchhoff (1824–1887) addressed these questions with two fundamental conservation laws for electric circuits: the law of conservation of energy and the law of conservation of charge.
Law of Conservation of Energy
As electrons move through an electric circuit they gain energy in sources and lose energy in loads, but the total energy gained in one trip through a circuit is equal to the total energy lost.
Law of Conservation of Charge
Electric charge is neither created nor lost in an electric circuit, nor does it accumulate at any point in the circuit.
By performing careful experiments, Kirchhoff was able to describe each of these conservation laws in terms of quantities easily measurable in electric circuits. They have since become known as Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL).
Kirchhoff’s voltage law (KVL):
Around any complete path through an electric circuit, the sum of the increases in electric potential is equal to the sum of the decreases in electric potential.
Kirchhoff’s current law (KCL):
At any junction point in an electric circuit, the total electric current into the junction is equal to the total electric current out.
Applying Laws and Math to Series Circuits
Kirchoff’s Current Law in Series Circuits:
It = I1 = I2 = In
Applying Laws and Math to Series Circuits
Kirchoff’s Voltage Law in Series Circuits:
Vtotal = V1 + V2 + V3 + … + Vn
Example
Vo = 240 V
Applying Laws and Math to Parallel Circuits
Kirchoff’s Voltage Law in Parallel Circuits:
V1 = V2 = V3 = Vtotal
Applying Laws and Math to Parallel Circuits
Kirchoff’s Current Law in Parallel Circuits:
Itotal = I1 + I2 + I3 + …
Example
Combining the two laws together:
Try the practice problems