Abstract—Inductors and transformers have been part of the most common practices in the field of electronics. From its discovery, existing technologies have been revolutionized and led to the technological advancements throughout the years. In this laboratory experiment, the students primarily aim to determine the characteristics of inductors and transformer through the variations of their operating frequencies. The students will also determine the essence of electromagnetic induction and its laws in using inductors and transformers. The experiment will be implemented with the use of laboratory materials, equipments and testing devices in line with the simulations using the LTSpice. Then, the students will create an inductor in which they will eventually use in creating a transformer. Lastly, the students will gather enough data, analyze, compare, and interpret the characteristics of an inductor and a transformer.

I. Introduction

Inductors have been part of the most common practices in the field of electronics. As it was discovered in 1830s, existing technologies have been revolutionized and led to the development of technological advancements throughout the years. From old inductor coils to the smaller and more efficient inductors, inductors have been utilized extensively in electronics particularly in analog circuits and signal processing. Inductors are also an important part of a transformer which has almost the same operational principles of electromagnetic induction. A transformer is a passive electronic component which uses the law of induction through conversion of electrical energy into another value. On the other hand, an inductor is also a passive electrical component which stores energy coming from a magnetic field caused by the passing of electric current. These two components both exhibit the law of induction but with different perspectives and the theory of operations of these components are to be presented after. In this laboratory experiment, the students are going to determine the characteristics of inductors and transformers under certain frequencies. The students are also going to determine the behavior of these components through variations in other elements affecting them. Lastly, the law of electromagnetic induction will be exemplified and demonstrated throughout the implementation of this laboratory experiment.

Basically, an inductor works when electricity starts to flow into the coil which causes a magnetic field to form. The more turns the coil is wound, the stronger the generated magnetic field will be. The magnetic field produced by an inductor also increases if the cross-sectional area of the inductor also increases.

Figure 1: Current and Magnetic Field in an Inductor

Imagine an AC current, which changes its direction periodically, flows inside the inductor. And when current flows to the inductor, the generated magnetic field causes the induced voltage to increase and this prevents further changes in the level of current. This is because in an inductor, the current does not change instantaneously.

Figure 2: Inductor Before and After Sudden Changes in Current

The essence of induced voltage in the inductor are still produced despite the change in the direction of current flow. The direction of current is also reversed before overcoming the induced voltage and this causes a no flow of current. On the other hand, if a DC current enters an inductor, the level of current does not change which means that there will be no induced voltage. This implies that an inductor allows DC and disallows AC to flow through it. Additionally, inductors also preserve current through the use of magnetic fields in storing energies and when AC voltage enters the inductor, current starts to lag behind the voltage based on the inductance and the frequency that relies on a phase angle.

Figure 3: Visualization of How a Transformer Works

A transformer is made up of primary and secondary windings with core laminations consist of strips. In between these strips, there are existing close gaps in the cross-section part of the core. Because of the coil being connected to an AC voltage, an electromotive force is induced in the transformer from the alternating flux in one of the laminated cores. Faraday’s law of electromagnetic induction is used in the transformer’s working principles. If we are going to close the second coil circuit, the current will flow and a magnetic transfer of electrical energy will occur from the first coil to the second coil. Moreover, the part where the AC supply comes from is called the primary winding and the part where the electrical energy came from is called the secondary winding. Overall, a transformer performs an electric power transfer from a single circuit to another without variations in frequency. And this occurs in line with the law of electromagnetic induction particularly the use of mutual induction.

II. Objectives

In this laboratory experiment, the students aim the following specific objectives:

· To create an inductor which will be used in inductance measurement

· To determine the non-ideal characteristics of an inductor

· To create a transformer using the inductors built

· To determine the behavior of a transformer over a range of frequencies

III. Calculations

In this section, the equations used and calculations made by the students were presented to show the concepts and ideas involved in the conduction of the laboratory experiment.

PART A:

Equations:

If d is very large than rC

(1)

If d is not very large than rC

(2)

Semi-empirical formula developed by H. A. Wheeler

(3)

Formula for the resistance of a wire

(4)

Calculations:

If d is very large than rC

(5)

If d is not very large than rC

(6)

Semi-empirical formula developed by H. A. Wheeler

(7)

Semi-empirical formula developed by H. A. Wheeler

(8)

PART B:

Equations:

In finding the initial resonant frequency of the circuit.

(9)

(10)

In finding the inductor from the better resonant frequency.

(11)

Formula for the percentage of the nearest inductor value to the measured inductance using the inductance bridge.

(12)

Calculations:

Calculated inductance

(13)

Measured inductance

(14)

The calculated inductance from the better resonant frequency

(15)

(16)

PART C:

Equations:

The formula for the equivalent series resistance of the inductor

(17)

The formula for the inductance of the inductor

(18)

The formula for the quality factor (Q) of the inductor

Calculations:

Sine wave

Equivalent series resistance:

(19)

Inductance of the inductor:

(20)

Triangle wave

Equivalent series resistance:

(21)

Inductance of the inductor:

(22)

Square wave

Equivalent series resistance:

(23)

Inductance of the inductor:

(24)

The quality factor of the inductor

(25)

IV. Simulations

In this section, the students have simulated and presented the schematic diagrams in each activity using the LTSpice. The simulations and their corresponding descriptions are here as follows:

A. Activity 1

In this activity, the students have simulated the schematic diagram for the inductor built. They have also determined the input and output voltages of the inductor built by setting its frequency at, below, and above its resonant frequency.