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# Voltage, current and Resistance calculations in series parallel and parallel series circuits

The electrical circuits are used in every electrical devices used by all people everyday. Many of these circuits are very complex and have a wide variety of elements and components that together operate a device such as household appliances or other devices.

Before working on complex circuit projects , you must start with the foundation, which is understanding the basics of voltage, electric current, electrical resistance , etc. It is essential to be able to differentiate between serial, parallel and parallel series connections.

This practice serves to check the theoretical knowledge studied in class about Ohm’s Law , the different types of connections, etc. In each process we carried out, the comparison between the theoretical data arising from the calculations made on paper, and the experimental data, which were those obtained in laboratory practice, can be observed.

These processes are explained step by step, answering the questions in the work guide, so that everything that has been done in practice has been analyzed, and a theoretical foundation and the mathematical analysis of each calculation are presented. It will be observed that the theoretical and experimental data are closely related and that both theory and practice are of great importance in the study of this subject.

## 1. OBJECTIVES

1.1. GENERAL OBJECTIVE

“Learn theoretically and experimentally to determine values of  voltage, electric current and resistance in elements that are connected in series, parallel and parallel series.”

1.2. SPECIFIC OBJECTIVES

• Practice using the multimeter.
• Apply Ohm’s Law and voltage divider to obtain values ​​of voltage, resistance and current.
• Learn to measure voltages, resistance values, and electric currents experimentally.
• Be able to assemble series parallel and parallel series circuits, identifying current and voltage properties that occur in each type of connection.

## 2. JUSTIFICATION

Understanding serial parallel, and parallel series connections is basic and fundamental for every electrical student. You cannot proceed with electrical projects if you do not know these concepts well and if you cannot determine voltage, resistance and current values, as well as the relationships between these values ​​in any type of connection.

This practice and the present report are justified in view of the need to learn the topics mentioned in the previous paragraph . At the end of it, it will have been well understood how what was studied theoretically is true when putting it into practice.

## 3. THEORETICAL FRAMEWORK

3.1. FUNDAMENTAL CONCEPTS

3.1.1. WHAT IS VOLTAGE

The potential difference between two points (1 and 2) of an electric field is called Voltage and is equal to the work carried out by said unit of positive charge to transport it from point 1 to point 2.

It is independent of the path traveled by the load (conservative field) and depends exclusively on the potential of points 1 and 2 in the field; is expressed by the formula:

where V1 – V2 is the potential difference, E is the field strength in Newton / Coulomb, r is the distance in meters between points 1 and 2, the same as the potential, in the International System of Units the potential difference is measures in volts. If two points that have a potential difference are connected by a conductor, an electric current flow will occur. Part of the charge with high potential will move through the conductor to the point of low potential and, in the absence of an external source (generator), this current will stop flowing when both points has equal electrical voltage (Henry’s Law). This transfer of charges is what is known as electric current.

The potential difference between two points in a circuit is also often referred to as a voltage drop. When an electric current can circulate through these points, the polarity of the voltage drop is determined by its conventional direction, that is, from the point of greatest potential to the point of least potential. Therefore, if  current I flows from resistance R in figure 1, from point A to point B, a voltage drop will occur in it with the indicated polarity and point A is said to be more positive that B.

Just because two points have the same electrical potential does not mean they have the same charge.

3.1.2. WHAT IS ELECTRIC CURRENT

It is the electric charge that passes through a section or conductor in the unit of time . In the International System of Units it is expressed in coulombs per second, a unit called the ampere.

If the intensity is constant over time, the current is said to be continuous; otherwise, it is called a variable. If no storage or load distribution occurs at any point in the conductor, the current is stationary. According to Ohm’s Law, the intensity of the current is equal to the voltage divided by the resistance that the bodies oppose:

3.1.3. WHAT IS ELECTRIC RESISTANCE

The electrical resistance, R, of a substance is defined as the opposition that the electric current encounters to travel through it. Its value is measured in ohms and is designated by the Greek capital omega (Ω). The matter has four states in relation to the flow of electrons. These are conductors, semi-conductors, resistors, and dielectrics. All of them are defined by the degree of opposition to the electric current (Electron Flow).

This definition is valid for direct current and for alternating current in the case of pure resistive elements, that is, without inductive or capacitive component. If these reactive components exist, the opposition presented to the current circulation is called impedance.

Depending on the magnitude of this opposition, the substances are classified as conductive, insulating, and semiconducting. There are also certain materials in which, under certain temperature conditions , a phenomenon called superconductivity appears, in which the resistance value is practically nil.

Electrical resistance is measured with the Ohmmeter, a device designed to measure electrical resistance in ohms. Because resistance is the potential difference that exists in a conductor divided by the intensity of the current that passes through it, an ohmmeter has to measure two parameters, and for this it must have its own generator to produce the electrical current.

3.1.4. THE OHM LAW

Since the electrical resistance in a circuit is very important in determining the intensity of the electron flux, it is clear that it is also very important for the quantitative aspects of electricity . It had discovered makes time that, equality of other circumstances, an increase in the resistance of a circuit is accompanied by a decrease in current. A precise statement of this relationship had to wait for reasonably safe measurement instruments to be developed . In 1820 Georg Simon Ohm, a school teacher German found that the current in a circuit was directly proportional to the potential difference the current produces, and inversely proportional to the current limiting resistance. Mathematically expressed:

where I is the current, V the potential difference and R the resistance.

This basic relationship is named after the physicist who intervened the most in its formulation: it is called Ohm’s Law.

If the proportionality sign of the Ohm’s Law is replaced by an equal sign, we have:

Ohm’s law to determine electric current (Amps)

Clearing the previous equation, two more equations are found :

Ohm ‘s Law to determine values of resistance (ohms)

Ohm’s law to determine voltage (Volts)

In this way, Ohm’s Law defines the unit of electrical resistance as well as the voltage and current, making simple clearances of the presented equations, as long as there are two known values ​​and a single unknown.

3.2. CONNECTION TYPES

3.2.1. SERIAL CONNECTION

Two or more resistors are connected in series when when applying a potential difference to the set, all of them are traveled by the same current. The scheme of connection of resistors in series is shown like image below:

3.2.2. PARALLEL CONNECTION

Two or more resistors are in parallel when they have two common terminals so that when applying a potential difference, UAB, all the resistors have the same voltage drop, UAB. A parallel connection is shown as follows:

3.2.3. PARALLEL SERIES CONNECTION

In a parallel serial connection you can find sets of resistors in series with sets of resistors in parallel, as shown below:

So, in same way series parallel can be acheived by connecting set of resistors in parallel and and then connecting them iwith set of resistors in series.

3.3. SERIES RESISTORS AND VOLTAGE DIVIDER

The voltage divider is a fundamental tool used when you want to know specific resistor voltages, when you know the total voltage across two resistors. It is necessary to consider that the voltage divider works to analyze two resistances, and that if you want to determine voltages of more than two resistances using the voltage divider, it should be done by adding resistances applying the voltage divider two by two, step by step, until arrive at the total number of resistances. This is very useful because in many occasions it is not possible to apply Ohm’s Law because you only have the value of the resistances, but the voltage is not known. It is then that the voltage divider is applied, with the following formulas and according to the scheme shown below:

Another important tool is the current divider, which works for parallel resistors. However, it was not necessary to use it in this practice, since it was in the parallel connections that the voltages (which were the same as the source because they were in parallel connection) and the values of the resistances were already available, so the currents were easily found through Ohm’s Law.

## 4. DEVELOPMENT AND SOLUTION OF THE WORK GUIDE USED ​​IN PRACTICE

coming soon…

### CircuitSchools Staff

We at CircuitSchools publish on basics of electronics and electric components and everything related to evolution of electrical technology with complete analysis of development boards and modules along with latest projects with innovative ideas.

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