If components in a circuit are connected consecutively, without any branches in the wiring, they are said to be connected in series. For example:
If one of the components is broken or disconnected the circuit is broken and the other components stop working. This is because the current will not be able to travel around the circuit.
IMPORTANT NOTE: This post deals with purely series circuits. It is possible to have a combination of components in series and parallel within the same circuit.
Current in a Series Circuit
Components connected in series each have the same current flowing through them, this is due to Kirchhoff’s First Law.
Where I1 is the current flowing through the first component, I2 is the current flowing through the second component and so on. This can be extended for as many components as there are connected in series.
Adding more components to a circuit will reduce the current flowing through each. Below is an example of 2 bulbs connected in series.
As you can see the current is the same at each point. If we add another bulb, the current flowing through each decreases:
Despite decreasing, the value of the current flowing through a component is the same as the others.
As well as the current being equal, the charge passing through each component is also the same in a given unit of time.
Potential Difference in a Series Circuit
Kirchhoff’s second law states that the sum of electromotive forces in a closed loop in a circuit must be equal to the sum of the potential differences. As the current flowing through the components of a series circuit remains the same, the potential difference across each component will vary if they have different resistances. Therefore:
Where Ɛ is the electromotive force of the circuit, V1 is the potential difference across the first component, V2 is the potential difference across the second component and so on.
This is as a result of the conservation of energy. The energy from the source must be shared between the individual components.
Resistance in a Series Circuit
The total resistance of a series circuit is equal to the sum of the resistances of each component in a circuit:
Where RTotal is the total resistance of the circuit, R1 is the resistance of the first component, R2 is the resistance of the second component and so on. The resistance of each component must be added to get the total, so if there were 10 components the equation above would go on until R10 was reached.
Worked Examples
Example 1
Calculate the potential difference across the resistor in the circuit below and state the value of the current flowing through the bulb.
Example 2
The total resistance of the below circuit is 95Ω. Calculate the resistance of resistor 2.
Example 3
Calculate the current in the below circuit.
This question requires knowledge of Ohm’s Law.
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