PHY12L | E301

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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.

PHY12L - E305 - ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

ANALYSIS ON ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

In experiment 305, which is entitled “Electric Fields and Equipotential Lines”, we studied the nature of electric fields by mapping the equipotential lines and then drawing in the electric lines of force using the conductive paper. The experiment was made easier with the help of the digital multimeter.

Electric field is defined as the electric force per unit charge. To determine the electric field E more precisely, consider a small positive test charge q at a given location.  As long as everything else stays the same, the Coulomb force exerted on the test charge q is proportional to q.  Then the force per unit charge, F/q, does not depend on the charge q, and therefore can be regarded meaningfully to be the electric field E at that point. We specify that the test charge q be small because in practice the test charge q can indirectly affect the field it is being used to measure. 

Coulomb’s law states that the electric force () is directly proportional to the magnitude of the charge (q) shown in the equation:

 

 

Or if shown by graph is,

The electric force () is also inversely proportional to the square of the distance of charges with each other (r) shown by the equation and the graph below.

 

 

 

 

 

 

 

 

 

 

 

 

 

Combining the two equations and removing the proportionality symbol, we will have the equation:

 

 

If, for example, we bring a test charge near the  Van de  Graaff generator  dome,  the Coulomb  forces from  the test charge redistribute charge on the conducting dome and thereby slightly change the E  field that the dome produces.   But secondary effects of this sort have  less and less  effect on the proportionality between F and q  as we make q  smaller. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.  Electric field lines can be drawn using field lines. They are also called force lines.

The field lines are originated from the positive charge. The field lines end up at the negative charge.

(Positive charge electric field)

                                                                                    

 

 

 

	(Negative charge electric field)

 

                                                                                                                  

A positive charge exerts out and a negative charge exerts in equally to all directions; it is symmetric. Field lines are drawn to show the direction and strength of field. The closer the lines are, the stronger the force acts on an object. If the lines are further each other, the strength of force acting on a object is weaker.

Closely associated with the concept of electric field is the pictorial representation of the field in terms of lines of force.  These are imaginary geometric lines constructed so that the direction of the line, as given by the tangent to the line at each point, is always in the direction of the E field at that 2 point, or equivalently, is in the direction of the force that would act on a small positive test charge placed at that point.  The electric field and the concept of lines of electric force can be used to map out what forces act on a charge placed in a particular region of space.

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and the electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces.

In some sources, definition of electric charge is a characteristic of some subatomic particles, and is quantized when expressed as a multiple of the so-called elementary charge e. Electrons by convention have a charge of −1, while protons have the opposite charge of +1.

In general, same-sign charged particles repel one another, while different-sign charged particles attract. This is expressed quantitatively in Coulomb's law, which states the magnitude of the repelling force is proportional to the product of the two charges, and weakens proportionately to the square of the distance.

The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function.

In physics, the space surrounding an electric charge has a property called an electric field. This electric field exerts a force on other charged objects. The concept of electric field was introduced by Michael Faraday.

The electric field is a vector with SI units of newtons per coulomb (N C-1) or, equivalently, volts per meter (V m-1). The direction of the field at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. Electric fields contain electrical energy with energy density proportional to the square of the field ntensity. The electric field is to charge as acceleration is to mass and force density is to volume.In the experiment, we are not required to solve for any values like the electric force or the intensity of electric field but rather we are asked to observe some properties of the electric field. We are able to do this by making a simple electric field that can be easily observed.  This can be done by using a conductive paper and a 6 volts battery to generate electric charges.  By using a silver ink pen, we are able to mark the electrodes on which the electric charges will pass.

 The objective of the experiments is to study the nature of electric fields by mapping the equipotential lines and then drawing in the electric lines of force. To start of the experiment, the materials used were conductive papers, silver ink pen, corkboard, push pins, connecting wires, circular template, digital multimeter and battery and as shown below:

 

 

 

	Conductive Paper
						Template, Push Pins and Wires
			Battery

 

 

 

 

 

The experiment consists of two parts. One is “Dipoles of Unlike Charges”. On the first part of the experiment, we searched for the points on the conductive paper that have equal potential. We have observed that when we connected the points with the same potential, the result is a parabola curve. We did five trials. The experiment is not very difficult since we have to find one point that has the same potential with the reference point. It requires patience.

Data obtained are the following:

Multimeter Reading (PART A)	Abscissa	Ordinate
.605 Volts	0	9
	-1	10.3
	-0.8	9.3
	-0.4	9.1
1.182 Volts	0	8
	-1.5	8.8
	-2.2	10
	-2.5	11
1.529 Volts	0	7
	-0.9	7.1
	-2.8	8
	-3.2	9
1.774 Volts	0	6
	-3.5	7.5
	-4.3	8
	-5.3	9
2.02 Volts	0	5
	-2.1	5.3
	-3.9	6
	-4.8	6.5

And as we graph the data, this figure was made. Showing that those blue lines were the data gathered, the equipotential lines form by the coordinates and by following the manual, that the electric field is perpendicular to the equipotential lines, those green lines were produced.

The distances of the equipotential lines are proportional to its distance to the point source. The closer the equipotential lines are to the source, the closer they are to each other.

          On the second part of the experiment, we followed the same procedure as the first. Here, instead of having on a point of negative charge, we made it surround the positive charge. The only difference is that we drew a circle that will serve as our guard ring and our point source is the origin. We have observed that after connecting the points with equal potential, the resulting figures were circles.

 

 

 

 

 

 

 

In this part, the following table was the results achived:

Multimeter Reading (PART B)	Abscissa	Ordinate
2.31 Volts	0	-1
	-1	-0.2
	-0.6	-0.9
	-0.8	-.07
3.47 Volts	0	-2
	-.08	-1.9
	-1.8	-0.9
	-1.5	-1
4.18 Volts	0	-3
	-1.6	-2.2
	-2.5	-1
	-2.8	-0.1
4.75 Volts	0	-4
	-1.2	-3.8
	-1.8	-3.4
	-2	-3.2
5.16 Volts	0	-5
	-0.9	-4.9
	-1.2	-4.8
	-1.5	-4.7

 

And the graph formed is below. Same formation and analyzation was made for blue lines were the data gathered, the equipotential lines form by the coordinates and by following the manual, that the electric field is perpendicular to the equipotential lines, those green lines were produced.

The small movement of the tester on the conductive paper will have a big movement on the reading of multimeter made the experiment slower and difficult.

Another thing is, tt is not possible for the equipotential lines to intersect each other, since they all follow the law of conservation of charge in which they must trade their charge to attain a new one.

          In the discussion of electric fields one can easily grasp its importance in our modern life from the compass used by early travelers to the technology used in our VCR’s. One example of which is electric motors which power our appliances and electric generators which produce electricity that run our world.

We can find electric fields in our everyday life and from there we can see the importance it has done for us.

The field generated in the experiment is produced from the special conductive paper, thus causing or making a hole in the paper would inevitably produce errors in the experiment. It is also a keen idea to take exact and precise measurements in order to make the graph as round as possible.

 

 

CONCLUSION ON ELECTRIC FIELDS AND EQUIPOTENTIAL LINES

Experiment 305, which is entitled “Electric Fields and Equipotential Lines”, aims to consider the nature of electric fields by mapping the equipotential lines and then drawing in the lines of electric lines of force.An electric field is an area where electrostatic force is present.On the other hand, equipotential lines are lines with equal potential.

          In the experiment, we used the conductive paper as the electric field. We plotted the points wherein the potentials are equal. The resulting figure was a parabola. We plotted the same coordinates on the negative x-axis. After doing five trials, we connected the five parabolas with a line intersecting perpendicularly. This is the electric line of force with direction from the positive to negative x-axis.

          We also plotted the points with equal potential on a guarded ring. Using the origin as our point source, we produced circles. This means that the electric lines are trapped inside the guard ring. The reason for this is that the guard ring can conduct electricity since it is made up silver. As we increase the distance from the point source, the voltage decreases.

In this experiment we can see that the equipotential lines generated are proportional in strength with respect to their distances from the point source, from this we can assume that the strength of the electric charge is proportional to its distance.