It may come as a surprise, but the first electric circuit was assembled back in 1800 by Alessandro Volta. He created a primitive circuit, which consisted of electrodes placed in water, and his invention - a battery. As the current was flowing through the water, hydrogen and oxygen were obtained. From that point onwards, the concept of electric circuits developed rapidly, as Thomas Edison invented the lightbulb, Friedrich Drexler built the first ammeter, and eventually all the electric circuit components as we know them now emerged. In this article, we'll develop a better understanding of all the nuance that comes with building a simple electric circuit and discuss the two main types of circuits: series and parallel.
Simple Circuit Definition
First, let's define what exactly is an electric circuit.
An electric circuit is composed of electrical loops which can include wires, batteries, resistors, lightbulbs, capacitors, inductors, switches, ammeters, voltmeters, etc.
When these electrical loops are closed, a current can flow through them. However, when it's open - there's no current flow possible.
There is a minimum of three types of elements needed for an electric circuit to work:
an energy source (e.g. a battery),
an energy consumer (e.g. a light bulb),
a conductive path (e.g. wires).
Once a functioning electric circuit is created, other elements such as inductors, ammeters, and switches can be added, depending on the purpose of the specific circuit.
Simple Circuit Diagram
Each circuit element has a common symbol that is used to create circuit diagrams. A list of the main elements is compiled in Figure 1 below.
Fig. 1 - The commonly used symbols of circuit diagram elements.
Some of these elements, like resistors, can be categorized as fixed or variable. A fixed resistor simply implies that its resistance remains constant and cannot be adjusted, while a variable resistor has adjustable resistance. Variable elements are indicated with a diagonal strike-through arrow.
The properties of a specific electric circuit depend on the arrangement and characteristics of each element. It is often necessary to connect several components to one source of electricity so that one element can be a part of several electrical loops simultaneously. They can be connected in series or in parallel. Let's look at both of these circuit types more in-depth.
Simple Series Circuit
One of the main ways of assembling electric circuits is by connecting elements in series.
A series connection is one in which circuit elements are connected such that any charge passing through one element must proceed through the other and has no other path available between them.
In a series connection, the same current \(I\) flows through all components. A potential difference \(V\) occurs on each of the elements and differs depending on their resistance.
Fig. 2 - A series circuit diagram consisting of three resistors.
For instance, if several resistors are connected in series as pictured in Figure 2 above, the sum of the individual voltages is the total supplied voltage. Here the circuit consists of three consumers, however, if we kept adding the general expression for total potential difference can be expressed as
\[ V_\text{series}=\sum_{i=1}^n V_i=V_1+V_2+ \dots,\]
where \(n\) indicates the number of consumers (in the example above, \(n=3\)).
That means that all the resistors in the series connection can be replaced by one equivalent consumer, whose potential difference can be found by using the total resistance of all the resistors together rather than individually. The equation for finding the total resistance of a series connection is
\[R_\mathrm{series}=\sum_{i=1}^nR_i=R_1+R_2+ \dots.\]
The more resistors are connected in a series circuit, the more resistance the whole system will have.
There are some disadvantages to a series circuit. If one of the elements within a series circuit stops working or gets disconnected, the whole circuit is immediately interrupted. Also, the supplied voltage is distributed among all the components proportionally, depending on their resistance. If one of the elements - for instance, the light bulb - requires a specific amount of voltage to glow, the source might not provide enough for it to work properly as other elements share the same voltage supply.
Simple Parallel Circuit
In a parallel circuit, the respective outputs of all components are connected to the corresponding pole of the power source, creating a branched electrical circuit.
A parallel connection is one in which charges may pass through one of two or more paths.
The electric current \(I\), flowing from the positive pole of the source, is divided among all elements and then merges again at the negative pole of the battery. In a parallel circuit, the potential difference \(V\) is the same across each path, provided by the electromotive force (emf) of the power source. An example of a parallel circuit consisting of three resistors can be seen in Figure 3 below.
Fig. 3 - A parallel circuit diagram consisting of three resistors.
From this example of a parallel circuit, we can obtain the general form of the three main properties of a circuit. The potential difference stays constant, while the total current is the sum of the current through the individual components:
\[ I_\text{parallel}=\sum_{i=1}^n I_i=I_1+I_2+\dots,\]
where \(n\) once again indicates the number of consumers.
Finally, the reciprocal of the total resistance is the sum of the reciprocals of all consumer resistances:
\[\frac{1}{R_\mathrm{parallel}}=\sum_{i=1}^n\frac{1}{R_i} =\frac{1}{R_1}+\frac{1}{R_2}+\dots.\]
One of the advantages of connecting elements in a parallel circuit is that the resistance can be reduced. Also, if one part of the circuit breaks, the current continues to flow in the others, unlike in the series circuit case. For instance, in an apartment, all light bulbs and electrical appliances are connected in parallel. Furthermore, each apartment in a building is then connected to the general electrical network in parallel. So, if one homeowner decides to do remodeling, they can turn the electricity off only in their unit.
Simple Circuit Examples
Let's look at an example problem, involving components both in series and parallel.
We have the following circuit consisting of three resistors as pictured in Figure 4.
Fig. 4 - An example circuit, where three resistors are connected both, in series and parallel to one another.
Simplify the resistors into a single resistor and calculate the current flowing through it, if the circuit is supplied with \(12\,\mathrm{V}\).
Answer
The \(3.2 \, \Omega\) and \(2.5 \, \Omega\) resistors are connected in series, so we use the equation
\begin{align}R_{\mathrm{series}}&= \sum_{i=1}^2R_i \\&= 3.2 \, \mathrm{\Omega} + 2.5 \, \mathrm{\Omega} \\ &= 5.7 \, \mathrm{\Omega}. \end{align}
Now, these two resistors can be replaced by a new \(5.7 \, \Omega\) resistor, which is parallel to the \(4.8 \, \Omega\) resistor, so we use
\begin{align} R_{\mathrm{parallel}}& = \left(\sum_{i=1}^2\frac{1}{R_i}\right)^{-1} \\ & = \frac{R_1 \, R_2}{R_1 + R_2}\\& = \frac{ 5.7 \, \Omega \times 4.8 \, \Omega}{5.7 \, \Omega + 4.8 \, \Omega}\\&= \frac{27 \, \Omega^2}{10.5 \, \Omega}\\& = 2.6 \, \Omega. \end{align}
The final circuit will now consist of a single resistor with a resistance of \(2.6 \, \Omega\).
Finally, let's apply Ohm's law to find the current:
\begin{align} I&=\frac{V}{R} =\frac{12\,\mathrm{V}}{2.6 \, \Omega} =4.6\,\mathrm{A}. \end{align}
Simple Circuit - Key takeaways
- An electric circuit is composed of electrical loops which can include wires, batteries, resistors, lightbulbs, capacitors, inductors, switches, ammeters, voltmeters, etc.
- When electrical loops are closed, a current is flowing through them. However, when it's open, there's no current flow possible.
- The properties of a specific electric circuit depend on the arrangement and characteristics of each element.
- A series connection is one in which circuit elements are connected such that any charge passing through one element must proceed through the other and has no other path available between them.
- In a series connection, a constant current flows through all components while the potential difference \(V\) differs depending on the resistance of each consumer.
- The total potential difference in a series circuit can be expressed as \(V_\text{series}=\sum_{i=1}^n V_i.\)
- A parallel connection is one in which charges may pass through one of two or more paths.
- In a parallel circuit, the electric current is divided among all elements depending on their resistance while, the potential difference stays the same across each path.
- The total current of a parallel circuit can be expressed as \(I_\text{parallel}=\sum_{i=1}^n I_i.\)
References
- Fig. 1 - Circuit diagram elements, StudySmarter Originals.
- Fig. 2 - A series circuit diagram, StudySmarter Originals.
- Fig. 3 - A parallel circuit diagram, StudySmarter Originals.
- Fig. 4 - A circuit diagram example, StudySmarter Originals.
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