Kirchhoff’s Voltage Law

A law of basic importance to the analysis of an electrical circuit is Kirchhoff’s voltage law. This law simply states that the algebraic sum of all voltages around a closed path or loop is zero. Another way of saying it: The sum of all the voltage drops equals the total source voltage. A simplified formula showing this law is shown below:

Notice that the sign of the source is opposite that of the individual voltage drops. Therefore, the algebraic sum equals zero. Written another way:

The source voltage equals the sum of the voltage drops

The polarity of the voltage drop is determined by the direction of the current flow. When going around the circuit, notice that the polarity of the resistor is opposite that of the source voltage. The positive on the resistor is facing the positive on the source and the negative towards the negative.

Figure 80 illustrates the very basic idea of Kirchhoff’s voltage law. There are two resistors in this example. One has a drop of 14 volts and the other has a drop of 10 volts. The source voltage must equal the sum of the voltage drops  around the circuit. By inspection it is easy to determine the source voltage as 24 volts.

Figure 81 shows a series circuit with three voltage drops and one voltage source rated at 50 volts. Two of the voltage drops are known. However, the third is not known. Using Kirchhoff’s voltage law, the third voltage drop can be determined.

Determine the value of E4 in Figure 82. For this example, I = 200 mA.

First, the voltage drop across each of the individual resistors must be determined.

Kirchhoff’s voltage law is now employed to determine the voltage drop across E4.

Using Ohm’s law and substituting in E4, the value for R4 can now be determined.