Voltage in Series Circuits (Sources, Formula & How To Add)

What are Voltages in Series?

A series circuit is defined as a connection in which two or more electrical components are linked in a chain, so only one path exists for the charge to flow. Voltage, or potential difference, is the difference in electric potential between two points of a circuit. This article discusses voltage in series circuits in detail.

The battery supplies energy to the circuit, allowing charge to flow and creating a potential difference between the circuit ends. A 2-volt cell, for example, creates a 2-volt potential difference across the external circuit.

The electric potential at the positive terminal sits 2 volts above that at the negative terminal. As charge flows from positive to negative through the external circuit, it loses those 2 volts of electric potential.

This loss is termed a voltage drop. It occurs when the electrical energy of the charge converts into other forms (mechanical, heat, light and so on) while passing through the circuit components such as resistors or other loads.

Consider a circuit with several resistors connected in series and powered by a 2 V cell. The total loss of electrical potential around the circuit is 2 V. Each resistor takes a certain voltage drop, and the sum of all the component drops equals 2 V, the voltage rating of the power source.

This balance is Kirchhoff’s voltage law: around any closed loop, the algebraic sum of the potential rises and drops equals zero. The individual drops therefore always add up to the source voltage.

Mathematically, we can express it as

By using Ohm’s law, the individual voltage drops can be calculated as

Now assume a series circuit comprising 3 resistors and powered by a 9V energy source. We will find the potential difference at different locations while the current passes through the series circuit.

The locations are marked in red colour in the circuit below. Current passes from the positive terminal of the source towards the negative terminal, and the negative sign of the voltage or potential difference represents a loss of potential across a resistor.

The electrical potential differences between points in the circuit can be drawn on an electric potential diagram, shown below.

In this example, the electrical potential at A = 9V because it connects to the higher-potential terminal, while the potential at H = 0V at the negative terminal. Passing through the 9V power source, the charge gains 9 V of potential from H to A. Traversing the external circuit, it loses that same 9 V completely.

The loss happens in three steps. A drop in voltage appears wherever the current passes through resistors, but no voltage drop occurs along plain wire. So between points AB, CD, EF and GH there is no voltage drop, while between points B and C the drop is 2V.

The source voltage of 9V therefore becomes 7V. Next, between points D and E, the voltage drop is 4V, taking the remaining voltage from 7V to 3V. Finally, between points F and G the drop is 3V, bringing the potential from 3V down to 0V.

Between points G and H the charge carries no electrical potential left. The power source restores it: as the charge travels from H back to A, the source returns the full energy boost for another pass through the circuit.

Multiple voltage sources in series can be combined into a single source by summing their voltages, considering their polarity.

AC Voltage Sources in Series

In the case of AC voltage sources in series, the sources can be added or combined into a single source provided the angular frequency (ω) of every connected source is identical. Sources of different angular frequencies cannot merge into one sinusoid; their instantaneous voltages still add, however, whenever the same current passes through all of them.

Application of Voltage in Series Circuits

The applications of voltages in series circuits include:

• Voltage divider.
• Fire alarm battery.
• Batteries in remote, toys etc.
• Lighting purposes in a train, Christmas tree etc.