Series Circuits
What is a Series Circuit?
A series circuit is an electrical circuit configuration in which the components, such as resistors, capacitors, and inductors, are connected in a sequential manner, forming a single pathway for the current to flow. In a series circuit, the same current flows through each component, and the total resistance is equal to the sum of the individual resistances.
Key characteristics of a series circuit include:
Single Path: In a series circuit, there is only one path for the current to flow from the power source to the load and back to the source.
Same Current: The current passing through each component in a series circuit is the same. This is because the current has no other alternative paths to take.
Voltage Divides: The total voltage supplied by the power source is divided among the components in a series circuit. The voltage across each component depends on its resistance or impedance.
Sum of Resistances: The total resistance in a series circuit is equal to the sum of the individual resistances of the components connected in series.
Decreasing Total Current: As more components are added to a series circuit, the total resistance increases, which in turn decreases the total current flowing through the circuit.
Component Dependency: If one component in a series circuit fails or is removed, the circuit becomes open, and the flow of current stops in the entire circuit.
Series circuits are commonly used in applications where the desired outcome is a controlled flow of current through each component. Examples include holiday lights, flashlight circuits, and some household electrical wiring systems. Understanding the behavior and properties of series circuits is fundamental in electrical engineering and circuit analysis, as it allows for the calculation of voltage drops, current distribution, and power consumption in the circuit.
Series Circuit Rules
A series circuit is defined as having only one path through which current can flow. From this definition, there are three rules for series circuits as follows:
All components share the same current
Resistances add to equal a larger, total resistance
Voltage drops add to equal a larger, total voltage.
Voltage drops add to equal total voltage.
All components have the same (equal) current. This is because there is literally only one path for current to flow.
Individual Resistances add to the total resistance.
Adding Resistance in Series
Adding resistance in series is as simple as it seems. According to the rules of Series circuits above, individual resistances add to the total resistance. This is because there is only one path for current to flow meaning each component with resistance will have the same current and have to share the total voltage of the circuit. All this said, the equation which you can probably deduce on your own is as follows:
Example
In this example, we have three resistors. This means we can shorten the equation above to be Rt = R1 + R2+ R3.
R1 = 470Ω R2 = 1K (1000Ω) R3= 2.2K (2200Ω)
Rt = 470 + 1000+ 2200 = 3670Ω
Adding Capacitance in Series
Understanding how to add capacitance in series takes a little more thought and understanding. If you need a deeper understanding of capacitors, see the Circuitree page on capacitors. By placing any capacitors in series, we are effectively spacing the plates of a capacitor at the start and end further from each other. If you think of this now as just one extra-wide capacitor, it makes sense that more distance between plates will decrease total capacitance. So, in the equation below, you will see that the total capacitance for capacitors in series will always add up to less than the smallest addend.
Example
In this example, we have four capacitors. This means we can shorten the equation above to be 1/Ct = 1/C1 + 1/C2 + 1/C3 + 1/C4.
C1 = 10µF (.00001) C2 = 100 µF (.001) C3= 1µF (.000001) C4= 1000µF (.01)
1/Ct = 1/.00001 + 1/.001 + 1/.000001 + 1/.01 = .000000908 F or .908 µF
A quick thing you can do when doing this math is to check that your answser is less than the smallest addend. In this case, everything checks out.
Voltage Drops
A Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated. The voltage drop across the electrical load is proportional to the power available to be converted in that load to some other useful form of energy. This can be seen clearly using a waterfall diagram like the one on the right. This shows the total potential voltage of a circuit and how each component causes a literal drop in voltage. All Voltage Drops should add up to the total voltage. No matter how much voltage there is or how many components there are in a series circuit, all voltage must be used. Sometimes this causes issues with power ratings and waste See the Power page for more details.
To the left is the formula for a voltage drop. Essentially, it is just the total voltage multiplied by the resistance in question divided by the resistance total. As you can see, it is just the proportion of Rx compared to Rt multiplied by the total available voltage.
Example
In this example, we have three resistors. We could do a voltage drop for any of these resistors, but let's arbitrarily pick R2. Let's also assume a 9V voltage source. Therefore V(R2) = Vt ( R2/ R1 +R2 + R3)
R1 = 470Ω R2 = 1K (1000Ω) R3= 2.2K (2200Ω)
V(R2) = 9V ( 1000/ 470 + 1000 + 2200) = 2.45 Volts
Voltage Divider
A voltage divider involves applying a voltage source across a series of two resistors. You may see it drawn a few different ways, but they should always essentially be the same circuit.
We’ll call the resistor closest to the input voltage (Vin) R1, and the resistor closest to ground R2. The voltage drop across R2 is called Vout, that’s the divided voltage our circuit exists to make.
Exercises
For exercises and projects that explore Series Circuits, see our Electronics Projects Page. The first set of activities are Resistors in a Circuit which expand on the concepts of Series Circuits like adding resistance, series current flow, voltage drops, and power over components.