PHY12L - E306 - SERIES AND PARALLEL CIRCUITS

ANALYSIS ON SERIES AND PARALLEL CIRCUITS

 

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches.

 

An electrical circuit is a network that has a closed loop, giving a return path for the current. A network is a connection of two or more components, and may not necessarily be a circuit. The three basic parts of a circuit are the source or the battery, resistors and a path specifically a conductor wire.

 

Electrical networks that consist only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines) can be analyzed by algebraic and transform methods to determine DC response, AC response, and transient response. A network that also contains active electronic components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools.

 

An alternating current (AC) is an electrical current whose magnitude and direction vary cyclically, as opposed to direct current, whose direction remains constant. The usual waveform of an AC power circuit is a sine wave, as this results in the most efficient transmission of energy. However in certain applications different waveforms are used, such as triangular or square waves.

 

Used generically, AC refers to the form in which electricity is delivered to businesses and residences. However, audio and radio signals carried on electrical wire are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal.

 

 

Direct current (DC or "continuous current") is considered as the constant flow of electrons in the single direction from low to high potential. This is typically in a conductor such as a wire, but can also be through semiconductors, insulators, or even through a vacuum as in electron or ion beams. In direct current, the electric charges flow in the same direction, distinguishing it from alternating current (AC). A term formerly used for direct current was Galvanic current.

 

 

 

 

 

 

 

 

 

 

 

The following graphs shows the relationships of direct current (DC) to alternating current (AC).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Series and parallel electrical circuits are two basic ways of wiring components. The names describe the method of attaching components that is one after the other or next to each other.

 

 It is said that two circuit elements are connected in parallel if the ends of one circuit element are connected directly to the corresponding ends of the other. If the circuit elements are connected end to end, it is said that they are connected in series. A series circuit is one that has a single path for current flow through all of its elements. A parallel circuit is one that requires more than one path for current flow in order to reach all of the circuit elements. Series circuits are sometimes called cascade-coupled or daisy chain-coupled. The current that enters a series circuit has to flow through every element in the circuit. Therefore, all elements in a series connection have equal currents.

 

The current in a series circuit is everywhere the same. Charge does NOT pile up and begin to accumulate at any given location such that the current at one location is more than at other locations. Current - the rate at which charge flows - is everywhere the same. It is the same at the first resistor as it is at the last resistor as it is in the battery. Mathematically, one might write,

 

 

On the other hand, total voltage is equal to the voltage in each the resistors on the circuit.

In addition, total resistance of the circuit is the sum of the resistance of each resistor present.

 

Sample parallel series

 When all the devices are connected using parallel connections, the circuit is referred to as a parallel circuit. In a parallel circuit, each device is placed in its own separate branch. The presence of branch lines means that there are multiple pathways by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through a single resistor present in a single branch. When arriving at the branching location or node, a charge makes a choice as to which branch to travel through on its journey back to the low potential terminal.

 

The current outside the branches is the same as the sum of the current in the individual branches. It is still the same amount of current, only split up into more than one pathway and can be written in the form,

 

 

If in the series circuits, the current is the constant variable, in parallel circuits, it is voltage. voltage is constant, total voltage is equal to the voltage in each resistor.

 

And lastly, resistance of a parallel circuit can be determined using the equation:

 

Voltages across components in parallel with each other are the same in magnitude and they also have identical polarities. Hence, the same voltage variable is used for all circuits elements in such a circuit. The total current I is the sum of the currents through the individual loops, found by Ohm's Law.

 

To start with the experiment, we need the following materials shown below.

 

 

 

 

 

 

 

 

 

 

The objective of the experiment was to tackle, distinguish and observe the principles, factors and characteristics of an electric circuit.  The experiment seeks to explain and for us to observe the two basic types of circuit connection.  They are the series and parallel circuits.  The two circuits are varying on how voltage, current and resistance will be computed based on their characteristics.  These will be explored on throughout the experiment.

 

 In part 1, we set up the apparatus for a series circuit by connecting the five batteries to the resistors, and then we set them to 60, 80 and 120 ohms. Each part has two sub-parts. We first need to identify the voltage of the series and then determine it's current. Using the volt meter, we measure the voltage and current of the series circuit in each of the resistance box.

 

The data gathered were:

 

Table 1. Series Circuit
	Experimental	Computed
Voltage Across Resistance 1 ()	1.419 V	1.350 V
Voltage Across Resistance 2 ()	1.900 V	1.800 V
Voltage Across Resistance 3 ()	2.840 V	2.700 V
Current Flowing through Resistance 1 ()	0.0225 A	0.02365 A
Current Flowing through Resistance 1 ()	0.0225 A	0.02375 A
Current Flowing through Resistance 1 ()	0.0225 A	0.02367 A
Total Current ()	0.0225 A	0.02369 A
Percentage Difference	5.02 %

 

The total resistance is 260 ohms and was obtained by just adding the three given ohms stated above. On the other hand, the total voltage was achieved by placing the VOM at the last part of the resistor.

 

We have a percent error of 5.02%. I found out that in a series circuit the voltage is increasing while the current is at constant. The voltage and the resistance are proportional to each other.

 

In part 2, we test the parallel circuit. Same resistance were used to find the values of the voltage and current of each of the resistance box.

 

We have a percent error of 2.47. When we compute the actual value of the voltage and current, I found out that voltage is constant in this kind of circuit and the current is decreasing, meaning that we have a positive result in our experiment that voltage is equal or near each other and the current is decreasing.

 

The total resistance is 26.67 ohms and was computed by adding the reciprocals of the three given resistance.

 

 

 

The complete data achieved is:

 

Table 1. Series Circuit
	Experimental	Computed
Voltage Across Resistance 1 ()	1.419 V	1.350 V
Voltage Across Resistance 2 ()	1.900 V	1.800 V
Voltage Across Resistance 3 ()	2.840 V	2.700 V
Current Flowing through Resistance 1 ()	0.0225 A	0.02365 A
Current Flowing through Resistance 1 ()	0.0225 A	0.02375 A
Current Flowing through Resistance 1 ()	0.0225 A	0.02367 A
Total Current ()	0.0225 A	0.02369 A
Percentage Difference	5.02 %

 

          The values of voltages measured across each resistor varies with the resistance, namely it increases in value as the resistance increases, as the formula shows,

 

 

The sources of error in this experiment are the wrong computation and the wire position. The resistance is a source of error because we are the one who will give the value of the resistance. Since, a battery can handle up to 100 ohms we must allocate the possible combination of each of the resistance box to avoid automatic reset from the battery.

 

Also, wire is an error in the experiment by means of allocating or putting the wire in a wrong formation. We must able to form a series and parallel circuit. If the wire position is incorrect, then the value that we can get is wrong and the volt meter can't read the voltage or current that we are experimenting.

 

Since this experiment is about voltage and circuits there are only a few errors that may cause the reliability of the result namely, the loose connections in the conducting wires and the wrong set-up of the conducting wires.

 

The electrical network established has many uses from your MP3 player to the computer you use at home, It is used in many homes like parallel circuits for appliances and lighting to name a few.

 

CONCLUSION ON SERIES AND PARALLEL CIRCUITS

The last experiment is about series and parallel circuits and the objectives were to determine the total current for both types of circuits, to determine the voltage and current on each resistor for both types of circuits were easily achieved by just following the procedure. The objectives, to observe the relationship of the total voltage and the voltage in each resistor for both circuits and to determine the relationship of the total current and the current in each resistor for both circuits was achieved by computing and analyzing the data gathered.

Resistance, current and voltage have a relationship depending on what type of circuit is it, either parallel or series circuit. In a series circuit we found out that the current here is constant and the voltage and resistance is directly proportional to each other. While in a parallel circuit we found out that voltage is constant and the resistance and current are inversely proportional to each other.

In series circuit, since the voltage is circulated in each resistor, the voltage is equal to the sum of all the voltage in each resistor. And because there is only one path for the charges to take and is passing through each resistor, the current flow is constant. And lastly, the total resistance is equal to the sum of the resistances present on the circuit. 

In parallel circuit, since each resistor is not passing by each other, and has their own pathway, the total voltage is equal to the voltage of each resistor, this time, this will be the constant.

 In performing the experiment, we must consider the connection of wires and relationship of the parallel and series circuit. Because considering the 2 factors can minimize the errors that we can obtain in the experiment.