Electrical Circuit Theory and Network Theorems

Approaches to Circuit Analysis

There are few theorems that can be applied to find the solution of electrical networks by simplifying the network itself or it can be used to calculate their analytical solution easily. The electrical circuit theorems can also be applied to A.C systems, with only one difference: replacing the ohmic resistance of the D.C system with impedance.

There are two general approaches to network analysis:

1. The Direct Method:

In this method, the network is left in its original form while determining it different voltages and currents. Such method are usually restricted to fairly simple circuits and include Kirchhoff’s law, loop analysis, nodal analysis, superposition theorem, compensation theorem, and reciprocity theorem, etc.

2. The Network Reduction Method:

In this method, the original network is converted into a much simpler equivalent circuit for a rapid calculation of different quantities. This method can be applied to a simple as well as complicated network. Examples of this method are: Delta/Star and Star/Delta conversion, Thevenin’s theorem, and Norton’s theorem, etc.

Understanding Basic Electronic Theory

When it comes to developing your own electronic projects, a prior knowledge of basic circuit theory becomes quite imperative. Read on to learn the bare essentials required for designing your own basic electronic circuits.

What is Basic Electronic Circuit Theory?

In simple terms, electronics may be understood as a branch of science that utilizes and controls the flow of electrons through specially designed networks of active and passive devices to produce a desired result. These networks are basically an interconnection of selected electronic components and constitute an electronic circuit. The electronic components involved are fundamentally classified as active and passive components. Active components play a live role in dimensioning or optimizing the flow of electrons through them as per their design specifications. These are all particularly semiconductor parts which include devices like LEDs, diodes, transistors, ICs, SCRs, triacs and many more, the list may be too long. The passive components are normally made up of carbon or chemical electrolytes and although not able to contribute actively yet play an important part in association with the active devices and complement them in every respect. Without these components, it probably won’t be feasible to design an electronic circuit. Components like resistors, capacitors, inductors etc. come under the passive electronic components.

How to Understand the Basic Electronic Components and Their Applications?

Diode: As shown in the picture a diode is a two terminal component and is recognized by a band or a ring at one of its ends.

In the symbol the band is indicated by a straight line at the arrow point. The lead which is terminating from this side is the cathode and the other one is the anode.

A diode will always allow a positive voltage to pass through its anode towards the cathode and block the other way round. Due to this particular characteristic, diodes are also used as rectifiers to convert AC into DC.

LED: LEDs are quite similar to the normal diodes as explained above, but sinceLEDs are able to emit light in the process, are specifically used as indicators and in other forms of lighting purposes. LEDs are unable to tolerate high currents and therefore always incorporate a series resistor to dimension the required minimum current through them.

Transistor: We all are quite familiar to this versatile member of the electronic family. Transistors are basically used to amplify small electrical signals and also for switching purposes.

Resistor: Since most semiconductor devices are sensitive to high currents, resistors are employed to restrict a correct flow of current through them. The values of these resistors are dimensioned by calculating them using various formulas.

The following examples will clearly explain regarding how basic electronic circuits are designed:

As shown in the figure, the trigger voltage which is generally received from an IC output or some other similar source is applied to R1. The received current is correctly optimized through R1 and is used to bias the transistor T1 so that it may conduct and light up the LED connected to its collector arm.

As explained above, resistor R2 has been incorporated to safeguard the LED from excessive currents. The value of R2 is calculated using the following formula:

R2 = (U_S - U_LED) ÷ I_LED

Here U_S = Supply Voltage,

U_LED = Minimum forward voltage drop of the LED used,

And I_LED = Current utilized by the LED for optimum brightness (normally 10 mA is found to be quite sufficient).

The value of R1 may be achieved using the following formula:

R1= (U_b - 0.6) × Hfe / I_LOAD

Here U_b = source voltage to R1,

Hfe = Forward current gain of T1 used (you may take the minimum value: 150)

I_LOAD = Current required to operate the collector load (a LED here).

The LED in the circuit may be easily replaced by a relay, in case it becomes necessary to switch heavy loads at the output. The base resistor value then may also be calculated appropriately using the above formula.

Sometimes we may find the source voltage to R1 too small and difficult for T1 to sense. During such conditions an interesting modification can be introduced by conjugating another transistor with T1 as shown in the adjoining figure. This configuration is termed as a Darlington pair.

Here the received weak signals are amplified to a suitable level by the first transistor and applied to the base of the next transistor which amplifies it sufficiently to energize the collector load.

Capacitor: It is another indispensable passive electronic component and inevitably finds a place in almost all electronic circuits. They are basically used to block DC and allow AC but may also find important applications in producing time delays, suppressing or filtering noise..

If a capacitor is linked with the above circuit, interesting results are obtained. The two adjoining figures may be explained respectively as follows:

In the first fig. T1 continues to conduct for quite some time even after the trigger voltage is cut OFF due to the charge stored inside C1, indicating how a capacitor is used in producing time delays.

The second circuit indicates how a capacitor can be used to produce a momentary pulse so that on receiving a base voltage the transistor and its collector load is switched ON only for an instant and then switched OFF. Here the trigger signal is allowed to pass instantaneously only during the charging process of C1 and inhibits its flow once C1 gets fully charged.

Well, I can just go on and on without ending as the topic of electronic basic circuit theory can be infinitely long. But for the time being, I will have to conclude here. Any raised eyebrows? Please let me know through your comments (comments need moderation, may take time to appear).

What is Electromagnetism and its Applications?

Electromagnetism is a branch of physics which deals with electricity and magnetism and the interaction between them. It was first discovered in the 19th century and has extensive application in today's world of physics.

Electromagnetism is the branch of physics that deals with electricity and magnetism and the interaction between them. It was first discovered in the 19th century and has extensive application in today's world of physics.

Electromagnetism is basically the science of electromagnetic fields. An electromagnetic field is the field produced by objects that are charged electrically. Radio waves, infrared waves, Ultraviolet waves, and x-rays are all electromagnetic fields in a certain range of frequency. Electricity is produced by the changing of magnetic field. The phenomenon is also called "electromagnetic induction." Similarly the magnetic field is produced by motion of electric charges.

The basic law of electromagnetism is known as "Faraday's law of Induction." The phenomenon of electromagnetism was discovered in the 19th century, and this led to the discovery of the "special theory of relativity" by Albert Einstein. According to his theory, electric and magnetic fields could be converted into one another with a relative motion. This phenomenon and its applications were discovered because of the many contributions from great scientists and physicists such as Michael Faraday, James Clerk Maxwell, Oliver Heaviside, and Heinrich Hertz. In 1802, an Italian scholar demonstrated the relationship between electricity and magnetism by deflecting a magnetic needle with electrostatic charges.

Electromagnetism is basically a conjecture of a combined expression of an underlying force, known as "electromagnetic force." This force can be seen when an electric charge is moving. This movement produces magnetism. This idea was presented by James Clerk Maxwell who published the theory of electricity and magnetism in 1865. Based on this theory many applications and other effects were discovered by other scientists. Electromagnetism has been extended to the area of quantum physics as well where light propagates as a wave and interacts as a particle.

It has been proved that electricity can give rise to magnetism and vice versa. A very simple example is that of an "electric transformer." The exchanges take place inside the transformer that gives rise to electromagnetic waves. Another fact about these waves is that they do not need a medium to propagate although their speed is relatively slower when traveling through transparent substances.

Electromagnetic Waves

Electromagnetic waves were first discovered by James Clerk Maxwell and they were confirmed after wards by Heinrich Hertz. Afterward, a wave form of electric and magnetic equations was derived by Maxwell which showed that the electric and magnetic fields had wave-like nature. The factors which differentiate electromagnetic waves from each other are frequency, amplitude and polarization. For example, a laser beam is coherent and the radiation is of only one frequency. There are other types of waves varying with their frequencies such as radio waves which are at very low frequencies and gamma rays and x-rays of very high frequency. Electromagnetic waves can propagate to very long distances and they are not affected by any kind of obstacles whether they are huge walls or towers.

This special interaction of electricity and magnetism has led to great advancements in modern science and technology, and efforts are being made to discover more about electromagnetism and its applications. Other forces are gravitational forces, strong and weak forces. Electromagnetism has also been combined with the weak force which is known as "Electroweak force."

Applications of Electromagnetism

Electromagnetism has numerous applications in today's world of science and physics. The very basic application of electromagnetism is in the use of motors. The motor has a switch that continuously switches the polarity of the outside of motor. An electromagnet does the same thing. We can change the direction by simply reversing the current. The inside of the motor has an electromagnet, but the current is controlled in such a way that the outside magnet repels it.

Another very useful application of electromagnetism is the "CAT scan machine." This machine is usually used in hospitals to diagnose a disease. As we know that current is present in our body and the stronger the current, the strong is the magnetic field. This scanning technology is able to pick up the magnetic fields, and it can be easily identified where there is a great amount of electrical activity inside the body.

The work of the human brain is based on electromagnetism. Electrical impulses cause the operations inside the brain and it has some magnetic field. When two magnetic fields cross each other inside the brain, interference occurs which is not healthy for the brain.

How to Make an Electric Lamp Circuit for a Science Project

You can easily make your own electric lamp circuit for a science project. The project does not use household current, depending instead on a safe size D battery as the power source. It’s a simple circuit made of a battery, wires and a light bulb, with the addition of a knife blade switch so that you can turn the light on and off. Utilizing these basic items will allow you to better understand how an electric circuit works.

1) Strip 1-inch of the insulation off both ends of each piece of copper bell wire. To do this, put each piece of wire in the notch of the wire stripper, leaving 1-inch of wire hanging out one side of the stripper. Close the handles of the wire stripper and rotate it around the wire, cutting through the insulation in the process. Open the wire stripper and pull off the insulation.

2) Connect one end of a 9-inch wire to one of the screw terminals on the knife blade switch. To connect the wires to the screw terminals, wrap the bare end of the wire around the base of the screw in a loop. Tighten the screw to hold the wire in place. Attach the other end of the wire to the positive terminal of the battery holder.

3) Attach another 9-inch wire to the second screw terminal on the knife blade switch. Open the switch by putting the movable blade in the upright, vertical position. Connect the other end of this wire to a screw terminal on the lamp holder.

4) Screw the light bulb into the lamp holder. Attach one end of the 18-inch wire to the remaining terminal on the lamp holder.

5) Connect the free end of the 18-inch wire to the negative terminal on the battery holder. Place the battery in the battery holder.

6) Push the movable blade of the knife blade switch in the down position to turn on the light bulb. The circuit is now closed, allowing the electricity to flow from the battery through the switch to the light bulb and back to the battery.

7) Turn off the bulb by pushing the movable blade of the knife blade switch to the upright, vertical position. This breaks the circuit and stops the electricity from lighting the bulb.

Quantum Physics: Disentangling Strange Behavior Of Qubits

Current technology enables the building of electrical circuits similar to those we use at home but reduced thousands of times in size to a micrometric scale of thousandths of a millimeter. When these circuits are built of superconductor materials and at near-absolute zero cryogenic temperatures, the world of everyday physics is left behind and the amazing world of quantum physics is entered. In this circuit the behavior is something like an artificial atom (i.e. like the so-called quantum bits ("qubits") of quantum computers) and the concepts of quantum optics, quantum information and condensed matter are mixed.

Electrical Science Projects for School

Electricity can provide some fascinating science projects for school, but students must be careful what they choose to tamper with when it comes to an electrical current. Without the proper knowledge and handling of electrical devices, such experiments are dangerous. However, there are some options for fun electrical science projects that are perfectly safe for students of all ages.

Electromagnet Strength

• Design a project that will test the strength of different electromagnets based on their design, according to All-Science-Fair-Projects.com.

  An electromagnet can be made easily by using an iron nail or bar wrapped tightly in coated copper wire. The wire should extend beyond each end of the nail and the wire should be applied in the same direction throughout. The ends of the wire must be stripped and connected to the positive and negative terminals on a battery. This will form the magnetic field.

  Complete the experiment by wrapping one bar 100 times with the wire and the next bar 75 times. Use the same material for the rest of the design.

  Use each magnet to try and pick up objects such as a pile of iron filings. Determine which, if either, of the magnets is most powerful by seeing which will hold the most filings.

Franklin's Bells

• Ben Franklin invented a machine known as Franklin's Bells to detect lightning storms many years ago, but you can build a model that works the same way with common household items, according to SciToys.com.

  Gather two empty soda cans, a plastic ballpoint pen, 5 inches of thread, a large square of aluminum foil, clear tape, a television and two coated wires.

  Take the pop-tops off each can and throw one away. Tie the end of the thread through the other one and tie the other end of the thread around the center of a ballpoint pen and tape it to secure it to the pen.

  Turn the soda cans upside down on top of a TV about three inches apart. Place the pen like a bridge between the cans. The pop-top should be dangling between the two cans. Tape the pen in place on the cans.

  Strip the ends of the wires and tape one end of a wire to one can and one end of the other wire to the other can. Turn on the TV and stick the aluminum foil to the screen (yes, it will stay there). Place one of the loose ends of wire under a corner of the foil on the television and grab the other loose end of wire with your bare hand.

  You will ground the wire with your hand, and the electricity used to light up the television screen will send the proper current to the cans. The pop-top will begin to go from can to can and ring the bell as it has detected electricity.

  The project works by sending the high voltage signal from the television to one of the cans. This charge gives one can a lot of free electrons, which attract the positive nuclei in the pop-top. The pop top jumps over to the can where it absorbs the charge until it equalizes with the can, then it falls loose and swings toward the other can. Since the other can is grounded, the charge is neutralized when contact is made and the pop-top pendulum swings back to its beginning positions and the cycle begins again.

Electrical Circuit Science Projects

Electrical circuits make interesting science projects. They can be very basic, involving only a few elements, or more complicated and ambitious. Electrical circuits can be used to explore different aspects of science such as electromagnetism, the generation of power, solar energy and electrochemistry. You can build your circuits from scratch using separate elements, or you can find electrical circuit kits that you can put together in different ways.

Basic Electrical Circuit

• A basic electrical circuit consists of a power source, usually a low-voltage battery; conductive wires; and something to show that current is flowing, such as a flashlight bulb in a holder. One conductor is attached to one terminal of the battery, the other conductor to the other terminal. The ends of the conductors are attached to the terminals of the bulb holder. Using a paperclip and two thumbtacks stuck in a piece of corrugated cardboard, you can make a simple switch to turn the current on and off.

Fruit and Vegetable Batteries

• You can use lemons, potatoes and other fruits or vegetables to generate small amounts of electric current. You will need two metal electrodes. A copper coin and a strip of zinc are commonly used: the greater the surface area of the electrode, the better. The acidic juice inside the lemon forms an electrolyte --- a liquid through which electricity can pass. Electrons move from one electrode to the other, producing a current. To make a circuit, you'll need to attach wires to the electrodes. Use the current from the lemon battery to power an electrical device; you can use a flashlight bulb for this, but since the current may be too small to light it, a small clock with an LCD display might be better. Connect several fruit or vegetable batteries together for a larger current.

Electromagnet

• A basic electromagnet is easy to build. Simply take a piece of ferrous metal, such as an iron nail, and wrap wire around it in coils. When you connect the ends of the wire to a power supply, such as a battery, the coiled wire induces an electromagnetic field in the metal core and it becomes a temporary magnet. The more coils, the stronger the magnet.

Electric Motor

• You can build your own direct current electric motor very easily. You'll need a permanent magnet, a battery, some copper wire, and two angled pieces of conductive metal with holes punched in them large enough for the wire to pass through easily. You'll need to make a coil of wire with the two ends sticking out from it. Set the angled strips of metal like bookends with the wire coil positioned in the middle so it hangs over the permanent magnet. Connect each of the battery terminals to one of the strips of metal. You should see the coil of wire spin around, as the electromagnetic field induced within the coils is repelled by the permanent magnet.

Solar Power

• You can obtain photovoltaic cells and small solar panels very cheaply. These can be used to power a number of devices, such as an electric radio. You can also use solar panels in experiments to demonstrate how the angle of the sun affects the amount of light falling on the panel, or how the current produced by the panel varies with the intensity of the light falling on it.

How EMF filters can protect your home

Electromagnetic fields, or EMFs, are emitted by all electronic devices. This means that EMFs are in your home, in your office, and even outside! Unfortunately, few people are aware of the dangers of overexposure to EMFs and even fewer know how to prevent it. EMF filters are a great way to keep your home safe and reduce the EMF exposure of your family.

Because information about EMFs can become highly technical, many people don't bother to read up on them, as they don't understand the information they find online. If you are in this camp, don't worry! Below are the answers to some common questions concerning EMFs and EMF filter use.

Electromagnetic Field FAQs

Q.:Why are EMFs dangerous?

A.:EMFs can be harmful because they can interfere with the delicate electrical system of your body. When this happens, a variety of health problems, ranging from trouble sleeping to the development of cancer, can take place. Additionally, people have reported fatigue, stress, irregular sensations in their skin, pains, muscle aches, burning eyes, difficulty thinking, digestive disorders, and infertility.

Q.:How can you reduce the EMFs in your home?

A.:Besides following tips to reduce EMF exposure, such as unplugging appliances when not in use and minimizing time spend on the computer and cell phone, EMF filters have been developed to reduce the amount of exposure you experience in your home. Electricity exists at several different frequencies, and the harmful frequencies are often called Dirty Electricity. EMF filters remove the Dirty Electricity from electrical lines, reducing the risk that you will be affected by it.

Q.:Do you need EMF filters in your house?

A.:No, however it is wise if you have electrical devices. Electronic devices could be leaking harmful EMFs into your home. Instead of living in fear of EMF exposure, you can use EMF filters to cut down the amount of radiation.

Q.:Do you need more than one EMF filter?

A.:Yes. Normally, 20 EMF filters are used in the average home; however, you can determine if you need more or less based upon the number of electronic devices that you have plugged into your outlets.

Q.:How long will my filters last?

A.:Because EMF filters are not like other commonly used filters, such as those in your car, they do not need to be replaced. Your EMF filters should last quite some time and only need repairs or replacement if they are damaged.

EMF Filter Expectations

Most people who use EMF filters report that they feel much better after the Dirty Electricity has been cleaned from their home. When using EMF filters, it is important for you to understand exactly what to expect. You will need to buy around 20 filters for them to be effective. Additionally, the filters may spark when you first plug them in. However, they should not make noise and should not have to be replaced unless they are somehow broken (i.e., stepped on).

The benefits of having EMF filters in your home are great, as you will be able to live free from the fear of overexposure to EMFs. Your health, sleep, and overall wellbeing may improve with the use of these filters. It is recommended that you consult with professionals before installing your EMF filters to ensure that you are using the right product in the right places. Once your filters start working, you may quickly notice the improvement!

With Electrical Stimulation to the Spinal Cord, Paralyzed Man Walks Again

Electrical impulses sent to a paralyzed man’s spinal cord allow him to walk again, researchers say. Rob Summers, 25, can voluntarily move his feet and hips and walk on a treadmill with support , in what could be a major breakthrough for the treatment of paralysis.

The research team, led by Dr. Susan Harkema of the University of Louisville, Ky., stressed that the treatment is not a cure for paralysis and that it worked with just one patient in one trial. But researchers not involved in the study say it is promising — one UK doctor told the BBC it was “mind-blowing.”

The findings appear to show that the legs and spinal cord, not the brain, are in control of movement. That means interruption of messages from the brain may not preclude paralyzed patients from walking again — they would just need new electrical signals to stimulate the spinal cord.

Summers appeared in various media outlets Friday to discuss the research.

Weeks after winning the College World Series with Oregon State University in 2006, Summers was hit by a drunk driver, suffering spinal cord damage that paralyzed him from the chest down. Neuroscientists implanted 16 electrodes in his spine, and sent electrical impulses to his lower spinal cord, mimicking the signals normally sent by the brain to initiate movement. Summers was suspended over a treadmill while the signals were transmitted to his spine. Writing in the British medical journal The Lancet , researchers say the spinal cord’s own neural network, combined with sensory information from his legs, is able to to control muscle and joint movement.

Summers trained for two years with a treadmill and physical therapists moving his legs to help him stand and walk.

V. Reggie Edgerton of the David Geffen School of Medicine at UCLA said sensory information is sent via neural networks in the legs directly to the spinal cord. The sensory feedback allows Summers to balance himself, bear his own weight and take steps over various speeds and directions, Edgerton said in a news release .

In a statement, Summers said the treatment has changed his life.

“For someone who for four years was unable to even move a toe, to have the freedom and ability to stand on my own is the most amazing feeling,” he said.

He was left with some sensation below the chest, so it’s not clear whether the treatment would work for spinal cord injury patients who experience no sensation. What’s more, Summers was an athlete in excellent physical condition before his injury, which could have helped his rehabilitation.

Still, his doctors hope that someday, patients with spinal cord injuries could use a portable electrical stimulation unit to move independently once again.

The work was funded by the National Institutes of Health and the Christopher & Dana Reeve Foundation.

The Strongest Electrical Current in the Universe Spotted, 2 Billion Light Years From Here

Galaxy 3C303, Keeping Current Generated from a Very Large Array image, this image shows the huge jet of current stretching for 150,000 light years across galaxy 3C303. Philipp P. Kronberg, Richard V.E. Lovelace, Giovanni Lapenta, Stirling A. Colgate via arXiv

Looking for a source of renewable electricity? Researchers at the University of Toronto have found some serious current emanating from a huge cosmic jet 2 billion light years from Earth. At 1018 amps, the current is the strongest current ever seen, equalling something like a trillion bolts of lightning.

The awesome current was found around the galaxy 3C303, whose core is the origin of a massive matter jet. While measuring the alignment of radio waves around 3C303, the researchers noticed a swift and sudden shift in the alignment of those radio waves, the telltale sign of an electrical current.

Why exactly this is happening is unclear, but the researchers speculate that the black hole at the galaxy’s heart plays a role, its magnetic fields generating this current that is so strong that it lights up the matter jet and helps to drive it outward. Way outward. The jet reaches out some 150,000 light years into interstellar space--farther than the estimated diameter of the Milky Way.