Kirchhoff’s Voltage Law in Series Circuits

The sum of all the voltage drops around a single closed path in a circuit is equal to
the total source voltage in that closed path.

In an electric circuit, the voltages across resistors, known as voltage drops, always exhibit polarities opposite to the source voltage polarity. For instance, when you follow a counterclockwise loop in the circuit, the source polarity is plus-to-minus, while each voltage drop is minus-to-plus.

In a circuit, the flow of current through resistors results in a loss of energy for electrons. As electrons traverse a resistor, they emerge at a lower energy level. The drop in energy creates a potential difference or voltage drop across the resistor, with a minus-to-plus polarity in the direction of the current.

Consider Figure 31, where the current flows out of the negative side of the source through the resistors. Electrons enter the negative side of each resistor and exit the positive side. The sum of the voltage drops across a closed path in a circuit is equal to the total source voltage in that path, as described by Kirchhoff’s voltage law.

Kirchhoff’s voltage law for a series circuit is expressed as:

Kirchhoff’s Voltage

This equation signifies that the sum of the voltage drops in a series circuit is always equal to the source voltage. You can verify this by measuring the voltage across each resistor and confirming that their sum equals the source voltage.

Kirchhoff’s voltage law holds true for any circuit, not just series circuits. The more general form of the law is:

This equation means that the algebraic sum of the voltages around any closed path in a circuit is equal to zero. If a voltage source is present, it is treated as one term in the summation.

This form can be applied to circuits other than series circuits, provided you follow a single closed path and assign the correct algebraic sign to each voltage in the path. In this more general application, voltages across resistors can be considered as either rises or drops, depending on the chosen path. The key is to maintain consistency in assigning signs as you traverse the path. For series circuits, the main principle remains: the source voltage (rise) equals the sum of the voltages (drops) across the resistors.

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