# In through the smaller, more restrictive pipes just

In this lesson, we’ll define what a series circuit is and compare it with a parallel circuit. Keep reading to see practical examples of series circuits, see descriptions of the components used, and get explanations of the concept of equivalent circuits.

## Definition

Have you ever wondered what is inside your cell phone, computer, television, or other electronic devices? Or how electrical engineers design and model the complex power system that supplies electricity to your home? All of these systems are made up of circuits.

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A circuit is the fundamental element in any electrical or electronic system. There are two ways to connect electrical components (such as resistors, capacitors, and inductors) in an electric circuit: series or parallel. The differences in these two methods affect the way current flows and the potential differences (or voltage) across components.

## Series Connection

A series arrangement of components has two distinguishing characteristics. In a series connection, the current is the same through each component regardless of what components are used or their values. The voltage drops across each component in the circuit are dependent upon the values of the components used in the circuit. Another way to view a series connection is that the positive end of each component is connected to the negative end of the previous component in a ‘one after the other’ arrangement. The negative end of each component is also connected to the positive end of the next component.Let’s compare it to water flow through pipes.

If we connect three pipes of different sizes together, the same amount of water (like current) flows through each pipe, but the pressure is proportional to the size of the pipe. The smaller, or more restrictive, pipes are similar to resistors with more resistance. The smaller pipes will have more pressure, and the larger resistor values will have a greater voltage drop. Likewise, larger pipes will have less pressure, just as smaller resistance values will have lower voltage drops.

## Parallel Connection

A parallel arrangement of components is the analogue of the series connection. In a parallel connection, the current in each parallel branch is dependent upon the values of the components used in the branch. The voltage, however, is the same across components.

In a parallel connection, the positive ends are connected to the positive ends, and the negative ends are connected to the negative ends.Let’s look at our analogy to water and pipes again. If we connect three pipes of different sizes together in a parallel configuration, the water splits off and travels in three different paths. The amount of water that flows through each path is proportional to the size of the pipe.

Water and current both take the path of least resistance. Less water flows through the smaller, more restrictive pipes just as less current flows through resistors with higher resistance values. The pressure, or potential difference, is the same in each pipe, just as the voltage is the same across all resistors in a parallel connection.

## Series Circuit

A series circuit is one in which every component is arranged in a series connection.

Therefore, a series circuit has the same current at all points in the circuit. The voltage drops across each component in the circuit sum to the source voltage. Also, all components of the same type may be combined to result in an equivalent value. The circuit would then consist of the voltage source and an equivalent component value.

If different components are used, each type of component may be combined to form an equivalent for that component type. This is commonly referred to as a series RLC circuit. For example, if the series circuit contains multiple resistors, inductors, and capacitors, each of these can be combined to result in a circuit that contains one equivalent resistor, one equivalent inductor, and one equivalent capacitor.An RLC circuit is often used to model an electrical power system because the power system consists of a series of resistive, inductive, and capacitive loads.

To simplify this for analysis and design, electrical engineers often reduce this to a series RLC circuit. If the series circuit consists of more than one voltage source, these sources can be summed to result in one combined voltage source.The advantages of a series circuit are that you can control the power delivered to the output. You can adjust the source voltage, add voltage sources, and/or adjust or add series components to achieve the desired output voltage and power.Like turning up the volume on a stereo, you are most likely changing the resistance value of a variable resistor in the circuit upstream from the speaker output.

If you decrease the resistance, then less voltage is dropped across the resistor and more across the output. This results in more volume.The disadvantages of a series circuit is that if one component fails, the entire circuit is rendered inoperable.

Like in Christmas tree lights, if all of the lights are connected in series and one light fails, none of the lights light up. If the lights are connected in parallel and one light goes out, the remaining lights remain lit because they still have a potential difference across them and the current can still flow in their branches.

## Equivalent Circuits

When resistors and inductors are connected in series, the equivalent value is found by adding all resistances and inductances together. For example, if three resistors of values 10, 100, and 1000 ohms are connected in series, the equivalent resistance is 1110 ohms. If two inductors of values 10 and 100 microHenries are connected in series, the equivalent inductance is 110 microHenries.Finding the equivalent capacitance of capacitors connected in series is a little different.

The equivalent capacitance is calculated from the formula 1/(1/C1 + 1/C2 + . . . + 1/CN), where C1 is the first capacitor, C2 is the second capacitor, and CN is the nth capacitor in the circuit.

For example, if the circuit contains three capacitors 0.82, 0.8, and 0.7 microfarads, the equivalent capacitance is calculated as:1/(1/0.82 + 1/0.8 + 1/0.

7) = 1/(1.22 + 1.25 + 1.43) = 1/3.9 = 0.

26 microfaradsIf the circuit contains more than one type of component, an equivalent value for each component must be calculated.

## Lesson Summary

The two methods of connecting an electrical circuit are:

1. A series connection in which the current is the same through each component in the circuit regardless of what components are used or their values. The voltage drops across each component in the circuit are dependent upon the values of the components used in the circuit.

2. A parallel connection in which the current in each branch is dependent upon the values of the components used but the voltage is the same across all components. A series circuit is one in which every component is arranged in a series connection.
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