INTRODUCTION

I. Resistor:

All materials possess electrical resistance, (opposition to the flow of electric current) to a

greater or lesser degree. Materials such as silver, copper and aluminum, which have

relatively low resistance, are called conductors, while materials such as plastics, glass, air

and rubber, which have high resistance, are called insulators. Between these two major

categories are a great variety of materials and alloys which have neither very high nor

very low resistance. There is no clear-cut dividing line between conductors and

insulators. Conductors gradually merge into resistors and resistors merge into insulators.

All materials, including conductors, have electrical resistance. A material has low

electrical resistance when it offers little opposition to the passage of an electric current.

The unit of electrical resistance is the ohm (Symbol Ω).

II. Capacitor:

Capacitance is that property of an electric device which tends to prevent a change in

voltage. The basic unit of capacitance is the farad. The farad is used in equations that include

capacitance terms. However, a farad is so large a quantity that measurements are made in

microfarads (µF) - one millionth of a farad. In electronic work the picofarad (pF) - one

millionth of a µF is a common unit.

If a dc voltage is applied suddenly to a capacitor a large current will flow. This

current will continue to flow at a decreasing rate until the capacitor is charged (the voltage

across the capacitor equals the source voltage). The current drops to zero as soon as the

capacitor voltage stabilizes (becomes constant), that is, when the capacitor is neither charging

nor discharging. The current can be quite large if the voltage across the capacitor changes

quickly. If the source voltage increases at a rapid rate, a large current will flow into the

capacitor to charge it. Under these conditions the capacitor acts as a load. Conversely, if the

source voltage decreases at a rapid rate, a large current will flow out of the capacitor, and the

latter behaves like a momentary source of power; in fact, just like a generator.

A capacitor has the ability to store electric energy by virtue of the electric field which

is set up between its plates. The quantity of energy stored depends upon the capacitance (in

farads) and upon the square of the voltage. When a capacitor is being charged, it receives and

stores energy, but does not dissipate it. When the unit is subsequently discharged, the stored

energy will be released until the voltage across the capacitor falls to zero.

A capacitor does not dissipate electric energy, it can only store it and then release it. This is

quite different from a resistor which cannot store energy, but can only dissipate it in the form

of heat.

These facts can help us to understand the behavior of a capacitor when it is connected

to an ac power source. The ac voltage is continually increasing, decreasing and reversing its

polarity.

When the voltage increases, the capacitor stores energy, and when the voltage

decreases, the capacitor must release it. During the "storing" period, the capacitor acts as a

load on the ac power supply but during the "releasing" period, the capacitor actually returns

its energy to the source. We have the very interesting situation where the capacitor

periodically acts as a source of power returning energy to the very supply which gave it its

energy in the first place.

In an ac circuit, power flows back and forth between the capacitor and its power

source and nothing useful is accomplished. If a wattmeter is placed between the power source

and the capacitor of the circuit shown in figure 5, power will flow from left to right when the

capacitor charges, and from right to left when it discharges.

Since no power is dissipated in the capacitor, the wattmeter will indicate zero. (It

actually tries to indicate positive when power flows from left to right and negative when the

power flow reverses, but the reversal takes place so quickly that the pointer does not have

time to respond).

The active power associated with an ideal capacitor is therefore zero. There will,

however, be a voltage drop across the capacitor and current will flow in the circuit. The

product of the two is the apparent power. The current leads the voltage by 90 electrical

degrees.

The reason the current leads the voltage can be easily seen. When the applied voltage

is going through its peak, the voltage for that instant is not changing hence, the current will

be zero. When the voltage is passing through zero it is changing most rapidly, hence, the

current is a maximum. Because of this unique condition, the apparent power is also called the

reactive power (var). Reactive power associated with capacitors carries a negative sign (-).

Capacitive reactance is the resistance offered to the flow of alternating current by the

presence of capacitance in the circuit. It is measured in ohms and is equal to the ratio E/l.

Reactance also depends upon the frequency and the capacitance in farads and can be

expressed mathematically as:

1XC =

2πfC

Where;

XC = capacitive reactance in ohms

C = capacitance in farads

f = frequency in Hertz (Hz)

2π = 6.28

The capacitance value can be found by rearranging the previous equation:

1C =

2πfXC

When two or more capacitors are connected in parallel the total capacitance is the sum of their individual capacitances:

CT = C1 + C2 + C3 + . . . . .

When two or more capacitors are connected in series the total capacitance is found by:

1 =

1 +

1 +

1 + . . . . .

CT C1 C2 C3

When only two capacitors are connected in series:

CT = C1 C2

C1 + C2

III. Inductors:

Inductors are frequently called chokes or coils and you should be familiar with the

three terms. Electric coils are essentially inductances designed to produce a magnetic field.

The entire electrical industry revolves, so to speak, around the electric coil. Coils are found in

motors, generators, relays and numerous other electric devices.

Inductance is that property of an electric circuit which tends to prevent a change in

current. Inductance is measured in henrys (H).

When a current flows through a coil a magnetic field is set up and this field contains

energy. As the current increases, the energy contained also increases. Conversely, when the

current diminishes, the contained energy is released, and falls to zero when the current is

zero.

The situation is analogous to the capacitor, except in a capacitor it is the voltage that

determines the amount of stored energy while in the inductor it is the current.

Consider, for example, the coil shown in the circuit of figure below. The ac power

source will cause an alternating current to flow in the coil, and this current increase,

decreases, changes its polarity and so on.

Consequently, the coil will receive energy from the source and then return it to the

same source depending upon whether the current is increasing or decreasing. In an ac circuit

power flows back and forth between the coil and the power source, without anything useful

being accomplished.

The wattmeter will read zero, for the same reason as when we had a capacitor for a

load. An ideal (perfect) coil will, therefore, not draw any active power. The active power

associated with an ideal inductor is therefore zero. There will, however, be a voltage drop

across the coil and current will flow in the circuit. The product of the two is the apparent

power.

The current lags behind the voltage by 90 electrical degrees. For the unique case

when this happens, the apparent power E x I is also called reactive power (var).

In order to distinguish the (-) var associated with a capacitor from that of an inductor,

inductive var carries a (+) sign.

Inductive reactance is the resistance offered to the flow of alternating current by the

presence of inductance in the circuit. It is measured in ohms and is equal to the ratio of E/I.

Reactance also depends upon the frequency and the inductance in henrys and can be expressed mathematically as:

XL = 2πfL

Where;XL = inductive reactance in ohms

L = inductance in henrysf = frequency in cycles per second (Hz)2π = 6.28

The inductance value can be found by rearranging the previous equation:

L = X

L / 2πf

When two or more inductors are connected in series the total inductance is the sum of their individual inductances:

LT = L1 + L2 + L3 + . . . . .

When two or more inductors are connected in parallel the total inductance is found by:

1 =

1 +

1 +

1 + . . . . .

LT L1 L2 L3

When only two inductors are connected in parallel:

LT =L1 L2

L1 + L2

In spite of the fact that a perfect coil would draw no active power from an ac source, we find that in

practice all coils will dissipate some active power, with the result that the wattmeter will not read

zero. This is because a coil always has some resistance and is, therefore, subject to I2R losses. Also

the iron cores associated with some coils are subject to iron losses, which is active power.

TUTORIALS

1. Connect all the resistors in parallel.

2. A capacitor having a capacitive reactance, XC of 250Ω draws a current of 3A when connected to a 50Hz, 500V source. Find the value of the capacitor.

XC=1

2 πfC

C= 12πf XC

¿ 12π (50Hz ) (250Ω )

¿12.732μF

3. Calculate the inductance of a coil having an inductive reactance, XL of 1200Ω at 50Hz. What would reactance be at direct current source?

X L=2πfL

L=XL

2πf

¿ 1200Ω2π (50Hz)

¿3.8197H

Experiment 11) Using the equations given in the introduction section, calculate the value of the single

equivalent resistance between terminal A and B for each of the following series and parallel resistor circuits. Show the calculations in the space provided. Record in the Table 1 below.

Circuit Requivalent

2400 Ω

3600

Ω

8400Ω

800Ω

685.71Ω

1714.285Ω

Experiment 2

1) Using the equations given in the introduction section, calculate the value of the single equivalent capacitance between terminal A and B for each of the following series and parallel capacitor circuits. Show the calculations in the space provided.

2) Record your calculations in the Table 2 below.

Circuits Cequivalent

CT =(20x40)/60 =13 pF

CT =(20x80)/100 =16 pF

CT =1/[(1/20)+(1/40)+(1/80)] =11.43 pF

CT =20+40=60 pF

CT =20+40+80=140pF

Experiment 3

1) Using the equations given in the introduction section, calculate the value of the single equivalent inductance between terminal A and B for each of the following series and parallel inductor circuits. Show the calculations in the space provided.

2) Record your calculations in the Table 3 below.

Circuit Lequivalent

LT = 1200+2400= 3600 H

LT = 1200+4800= 6000 H

LT = 1200+2400+4800= 8400 H

1/LT = [(1/1200)+(1/2400)] = 800 H

Experiment 4

Figure 8

Using standard resistor, measure the value of these resistors using portable double bridge. Record all the values in the table 5 below.

Standard value (Ω) Experiment value (Ω)0.1 0.110 10

100 100Table 5

Figure 10

Using standard resistor, measure the value of these resistors using multimeter. Record all the values in the table 8 below.

Standard value (Ω) Experiment value (Ω)0.1 0.110 10

100 100Table 8

CONCLUSION

In conclusion, we have learned the symbols of basic electrical elements, we have

determined the calculations of the single resistance which is equivalent to a group of resistor

connected in series and parallel, calculations of the single inductive reactance which is

equivalent to a group of inductors connected in series and parallel, calculations of the single

capacitive reactance which is equivalent to a group of capacitors connected in series and parallel.

Furthermore, we have also learned on how to use the Portable Double Bridge, Precision Double

Bridge and multimeter to measure an unknown resistor. For experiment 4, the experiment values

(Ω) were calculated and were written down and it was observed that the results noted down were

to prove how close the experiment values are to the standard values. The results mentioned have

very much supported by the theory stated, thus it can be deduced that the objectives of this

experiment were achieved which are to identify the symbols of basic electrical elements, to

calculate the single resistance which is equivalent to a group of resistor connected in series and

parallel, to calculate the single inductive reactance which is equivalent to a group of inductors

connected in series and parallel, to calculate the single capacitive reactance which is equivalent

to a group of capacitors connected in series and parallel and to operate Portable Double Bridge,

Precision Double Bridge and multimeter to measure an unknown resistor.

DISCUSSION

This experiment is all about knowing the symbols of basic electrical elements, calculating the

single resistance which is equivalent to a group of resistor connected in series and parallel,

calculating the single inductive reactance which is equivalent to a group of inductors connected

in series and parallel, calculating the single capacitive reactance which is equivalent to a group of

capacitors connected in series and parallel and operating Portable Double Bridge, Precision

Double Bridge and multimeter to measure an unknown resistor. The variables involved in this

experiment are resistance (Ω), inductance (H), capacitance (pF), and experiment values (Ω).

The first experiment is to calculate the single resistance which is equivalent to a group of

resistors connected in series and parallel. The second experiment is to calculate the single

capacitance which is equivalent to a group of capacitors connected in series and parallel. The

third experiment is to calculate the single inductance which is equivalent to a group of inductors

connected in series and parallel. The fourth experiment is to measure an unknown resistor using

Precision Double Bridge and Portable Double Bridge.

For the first experiment, the values of the single equivalent resistance between terminal A

and B for each of the following series and parallel resistor circuits were calculated as shown in

Table 1 (Refer to Appendices).

For the second experiment, the values of the single equivalent capacitance between

terminal A and B for each of the following series and parallel capacitor circuits were calculated

as shown in Table 2 (Refer to Appendices).

For the third experiment, the values of the single equivalent inductance between terminal

A and B for each of the following series and parallel inductor circuits were calculated.

For the fourth experiment, Portable double bridge is designed for measuring low

resistance from 0.1m Ω to 110 Ω with four multiplication plugs and one measuring dial. The

internal battery terminal (INT BA) as well as the P 2S terminals were shorted securely. The

power supply toggle switch BA was turned off and the RX terminal was opened. The GA

sensitivity dial was switched to CH to check the galvanometer driving battery voltage. The GA

sensitivity dial was then switched to G 0 until the pointer indicates 0 on the scale. An unknown

resistance was connected to the RX terminal as shown in Figure 1 (Refer to Appendices). Then,

the multiplying plug was inserted to the appropriate position using Table X (Refer to

Appendices) for the approximate resistance value. The measuring dial was set to G 2 and the BA

switch was turned on. Then, the GA switch was depressed momentarily and the direction of the

galvanometer deflection was observed. With each approach towards 0, the GA sensitivity was

moved to G 0 through G 1. When the pointer rests at 0, and the sensitivity dial is already at G 0,

the reading of the measuring dial was recorded. The RX value can now be obtained through a

specific formula (Refer to Appendices). Through the RX formula, the experiment value (Ω) can

be obtained and compared to the expected value, the standard value (Ω).

For the first experiment (Table 1), the values of the Requivalent are 2400 Ω, 3600 Ω, 8400 Ω,

800 Ω, 685.7 Ω, and 369.2 Ω. As for experiment 2 (Table 2), the values of C equivalent are 13 pF, 16

pF, 11.43 pF, 60 pF, and 140 pF. For experiment 3 (Table 3), the values of L equivalent are 3600 H,

6000 H, 8400 H, 800 H, and 685.7 H. For experiment 4 (Table 4), the experiment values

calculated for each of the standard values of 0.1 Ω, 10 Ω, and 100 Ω are 0.1 Ω, 10 Ω, and 100 Ω

respectively. The tables, calculations and formulae are shown in the Appendices.

The components used in carrying out this experiment are the resistors, Portable Double

Bridge, and connection leads. All these components (devices and tools) have their own

specifications in assisting the whole instrument in conducting the experiment. As closure, all

components definitely support in getting the most precise and accurate recordings and has a great

value and huge impact in completing this experiment.

Theoretically speaking, an electrical symbol is a pictogram used to represent various

electrical and electronic devices (such as wires, batteries, resistors, and transistors) in a

schematic diagram of an electrical or electronic circuit. An electrical drawing is a type of

technical drawing that shows information about power, lighting, and communication for an

engineering or architectural project. Any electrical working drawing consists of lines, symbols,

dimensions, and notations to accurately convey an engineering’s design to the workers, who

install the electrical system on the job. Besides that, an electrical circuit is a path in which

electrons from a voltage or current source flow. Electric current flows in a closed path called an

electric circuit. The point where those electrons enter an electrical circuit is called the "source" of

electrons. The point where the electrons leave an electrical circuit is called the "return" or "earth

ground". The exit point is called the "return" because electrons always end up at the source when

they complete the path of an electrical circuit. The part of an electrical circuit that is between the

electrons' starting point and the point where they return to the source is called an electrical

circuit's "load". Moreover, an electrical regulation is the process of the promulgation,

monitoring, and enforcement of rules, established by primary and/or delegate legislation and/or

the written instrument containing rules having the force of law on electrical bases.

There are several possibilities that might have contributed to the errors that occurred

during the experiment. Among those errors is physical errors (caused by experimenters). The

experimenters might not have waited for the readings to stabilize first and have recorded down

the wrong readings, which could lead to an abnormal trend of results. Not just that, the

experimenter may not have focused well during the experiment and may have recorded down

readings of the parameter in the field of another parameter. Furthermore, connection leads may

be put into the wrong coordination on the circuit board thus resulting in major errors. By doing

so, the recordings will be inaccurate and the ideal expected results could not be achieved.

Technical errors (caused by machineries/ instruments/ components) may have contributed to the

errors in this experiment. The Portable Double Bridge may be faulty without realization of the

experimenters. In addition to that, the connection leads may have not been in a perfect condition

in which are not suitable for the conduction of the experiment. This may cause disrupted

measurements by which bring towards more errors during the calculation of the prime variables.