Tag Archive | "alternating current"

Introduction to the Inductor

Hello everyone!

Today we are going to explore the use of the Inductor. This is a continuation from the series of articles on alternating current. An inductor is a component that can resist changes in AC current, and store energy in a magnetic field from a current that passes through it. A changing current (AC) causes a changing magnetic field which induces a voltage that opposes the current produced by the magnetic field. This is known as the inductance.  One could think of an inductor as an AC resistor. But first of all, what is an inductor comprised of?

In simple terms an inductor is a coil of wire, wrapped around a core. The core forms a support for the coil of wire – such as ceramic cores, or in some cases can affect the properties of the magnetic field depending on the chemical composition of the core. These may include cores formed from ferrite (usually zinc and manganese, or zinc and nickel) or powdered iron (which has a tiny air gap allowing the core to store a higher level of magnetic flux (the measure of magnetic field strength)allowing a higher level of DC current to flow through before becoming saturated.

So, the amount of inductance is influenced by several factors – the core material (as above), the size and shape of the core, as well as the number of turns of wire in the coil and its shape. The unit of inductance is the henry (H), however common values are usually in the millihenry (mH) or microhenry (uH) range.

Furthermore, there is an amount of DC resistance due to the properties of the coil wire, however this is usually negligible and kept to a minimum. For example, looking at a data sheet for a typical line of inductors – inductors.pdf – the DC resistance of a 10uH inductor is a maximum of 0.05 ohms. With inductors of higher values, the DC resistance will need to be taken account of. But more about that later.

This is the usual symbol for an inductor in a schematic:

However this may also be used:

And here is a variety of inductors in the flesh:

10microhenryss

radial ferrite core, generally for PCB use, handles around 1.5 amperes

radial leaded, very low resistance, handles around 2.5 amperes

ferrite core, convenient for through-hole PCB

phenolic core

toroidal – handles large currents ~10 amperes depending on model

surface-mount, can still handle around 500 mA

All of the pictured inductors have an inductance of 10 uH. Now let’s examine how inductors work with alternating current. Consider the following circuit:

1

 

Just like capacitors in AC circuits, an inductor has a calculable reactance. The formula for the reactance (X, in ohms) of an inductor is:


where f is the frequency of the AC and L is the value of the inductor in Henries (remember that 1uH is 10 to the power of -6). The formula to calculate the impedance of the above circuit is:

where Z is in ohms. And finally, the formula for AC Vout is

The formula for DC Vout is the usual voltage dividing formula. In this case, as we consider the inductor to not have any resistance, DC Vout = DC Vin.

So, let’s work through an example. Our DC Vin is 12 volts, with a 2V peak to peak AC signal, at a frequency of 20 kHz. The resistor R has a value of 1 kilo ohm, and the inductor L is 10 millihenries (0.01 H). A quick check of the data sheet shows that the 10 mH inductor has a resistance that cannot be ignored – 37.4 ohms. So this must be taken into account when calculating the DC Vout. Therefore we can consider the inductor to be a 37.4 ohm resistor when calculating the DC Vout, which gives us a result of 11.56 volts DC. Substituting the other values gives us a reduced AC signal voltage of 1.24 volts peak to peak.

Another interesting fact is that there is a relationship between AC Vout and the frequency of the AC signal. In the video below, I have used a 10k ohm resistor and a 10 uH inductor in the circuit described above. The frequency counter is measuring the frequency of AC Vin, and the multimeter is measuring the AC Vout:

This is an interesting relationship and demonstrates how an inductor can resist alternating current, depending on the frequency.

Thus ends our introduction to the inductor. We will continue with the inductor in the near future. I hope you understood and can apply what we have discussed today. As always, thank you for reading and I look forward to your comments and so on. Furthermore, don’t be shy in pointing out errors or places that could use improvement, you can either leave a comment below or email me – john at tronixstuff dot com.

Please subscribe using one of the methods at the top-right of this web page to receive updates on new posts. Or join our Google Group and post your questions there.

Posted in education, inductor, learning electronics, lesson, test equipment, tutorialComments (0)

Education – Introduction to Alternating Current – part two

Hello everyone

Today we are going to continue exploring alternating current, with regards to how resistors and capacitors deal with AC. This chapter is part two, chapter one is here. Once you have read this article, continue on with learning about inductors. To help with the explanations, remember this diagram:

sin2

That is, note that there are three possible voltage values, Vpp, Vp and Vrms. Moving on. Alternating current flows through various components just like direct current. Let’s examine some components and see.

First, the resistor. It operates in the same way with AC as it does DC, and the usual calculations apply with regards to Ohm’s law, dividing voltage and so on. However you must keep in mind the type of voltage value. For example, 10Vrms + 20Vpp does NOT equal 30 of anything. But we can work it out. 20Vpp is 10Vp,  which is 7.07Vrms… plus 10Vrms = 17.07Vrms. Therefore, 10Vrms + 20Vpp = 17.07Vrms.

Furthermore, when using Ohm’s law, or calculating power, the result of your equation must always reflect the type of voltage used in the calculations. For example:

scan1

Next, the capacitor. Capacitors oppose the flow of alternating current in an interesting way – in simple terms, the greater the frequency of the current, the less opposition to the current. However, we call this opposition reactance, which is measured in ohms. Here is the formula to calculate reactance:


the result Xc is measured in Ohms, f is frequency is Hertz, and C is capacitance in Farads. Here are two examples – note to convert the value of the capacitor back to Farads

 

scan3

scan4

Also consider if you have identical frequencies, a smaller capacitor will offer a higher resistance than a larger capacitor. Why is this so? A smaller capacitor will reach the peak voltages quicker as it charges in less time (as it has less capacitance); wheras a larger capacitor will take longer to charge and reach the peak voltage, therefore slowing down the current flow which in turn offers a higher reactance.

Resistors and capacitors can also work together as an AC voltage divider. Consider the following schematic:

As opposed to a DC voltage divider, R2 has been replaced with C1, the 0.1 uF capacitor. In order to calculate Vout, we will need the reactance of C1 – and subsitute that value for R2:

scan61

 

However, once the voltage has been divided, Vout has been transformed slightly – it is now out of phase. This means that Vout oscillates at the same frequency, but at different time intervals than Vin. The easiest way to visualise this is with an oscilloscope, which you can view below:

Please note that my CRO is not in the best condition. In the clip it was set to a time base of 2 milliseconds/division horizontal and 5 volts/division vertical.

Thus ends chapter two of our introduction to alternating current. I hope you understood and can apply what we have discussed today. As always, thank you for reading and I look forward to your comments and so on. Furthermore, don’t be shy in pointing out errors or places that could use improvement, you can either leave a comment below or email me – john at tronixstuff dot com.

Please subscribe using one of the methods at the top-right of this web page to receive updates on new posts. Or join our Google Group and post your questions there.

Posted in AC, alternating current, education, learning electronics, lesson, tutorialComments (1)

Education – Introduction to Alternating Current

Hello everyone!

Today we are going to introduce the basics of AC – alternating current. This is necessary in order to understand future articles, and also to explain in layperson’s terms what AC is all about. So let’s go!

AC – Alternating Current. We see those two letters all around us. But what is alternating current? How does current alternate? We know that DC (direct current) is the result of a chemical reaction of some sort – for example in a battery, or from a solar cell. We know that it can travel in either direction, and we have made use of it in our experimenting. DC voltage does not alter (unless we want it to).

Therein lies the basic difference – and why alternating current is what is is – it alternates! 🙂 This is due to the way AC current is created, usually by a generator of some sort. In simple terms a generator can be thought of as containing a rotating coil of wire between two magnets. When a coil passes a magnet, a current is induced by the magnetic field. So when the coil rotates, a current is induced, and the resulting voltage is relative to the coil’s positioning with the magnets.

For example, consider the diagram below (exploded view, it is normally more compact):

generator

This is a very basic generator. A rotating coil of wire is between two magnets. The spacing of the magnets in real life is much closer. So as the coil rotates, the magnetic fields induce a current through the coil, which is our alternating current. But as the coil rotates around and around, the level of voltage is relative to the distance between the coil and the magnet. The voltage increases from zero, then decreases, then increases… as the coil constantly rotates. If you were to graph the voltage level (y-axis) against time (x-axis), it would look something like below:

sin1

That graph is a sine wave… and is a representation of perfect AC current. If you were to graph DC voltage against time, it would be a straight horizontal line. For example, compare the two images below, 2 volts DC and AC, shown on an oscilloscope:

2v-dc-cro-small

2 volts DC

The following clip is 2 volts AC, as shown on the oscilloscope:

So as you can see, AC is not a negative and positive current like DC, it swings between negative and positive very quickly. So how do you take the voltage measurement? Consider the following:

sin2

The zero-axis is the point of reference with regards to voltage. That is, it is the point of zero volts. In the oscilloscope video above, the maximum and minimum was 2 volts. Therefore we would say it was 2 volts peak, or 2Vp. It could also be referred to as 4 volts peak to peak, or 4Vpp – as there is a four volt spread between the maximum and minimum values of the sine wave.

There is another measurement in the diagram above – Vrms, or volts root mean squared. The Vrms value is the amount of AC that can do the same amount of work as the equivalent DC voltage. Vrms = 0.707 x Vp; and Vp = 1.41 * Vrms. Voltages of power outlets are rated at Vrms instead of peak as this is relative to calculations. For example, in Australia we have 240 volts:

241vacs

Well, close enough. In fact, our electricity distributor says we can have a tolerance of +/- 10%… some rural households can have around 260 volts. Moving on…

The final parameter of AC is the frequency, or how many times per second the voltage changes from zero to each peak then back to zero. That is the time for one complete cycle. The number of times this happens per second is the frequency, and is measured in Hertz (Hz). The most common frequency you will hear about is your domestic supply frequency. Australia is 50 Hz:

50-hzss

… the US is 60 Hz, etc. In areas that have a frequency of 60 Hz, accurate mains-powered time pieces can be used, as the seconds hand or counter can be driven from the frequency of the AC current.

The higher the frequency, the shorter the period of time taken by one cycle. The frequency and time are inversely proportional, so frequency = 1/time; and time – 1/frequency. For example, if your domestic supply is 50 Hz, the time for each cycle is 1/50 = 0.02 seconds. This change can be demonstrated quite well on an oscilloscope, for example:

In the video above there is 2 volts AC, and the frequency starts from 100 Hz, then moves around the range of 10 to 200 Hz. As you can see, the amplitude of the sine wave does not change (the height, which indicates the voltage) but the time period does alter, indicating the frequency is changing. And here is the opposite:

This video is a demonstration of changing the voltage, whilst maintaining a fixed frequency. Thus ends the introduction to alternating current. In the next instalment about AC we will look at how AC works in electronic circuits, and how it is handled by various components.

I hope you understood and can apply what we have discussed today. As always, thank you for reading and I look forward to your comments and so on. Furthermore, don’t be shy in pointing out errors or places that could use improvement.

Please subscribe using one of the methods at the top-right of this web page to receive updates on new posts. Or join our Google Group and post your questions there.

Posted in AC, alternating current, education, learning electronics, lesson, safety, tutorialComments (0)


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