The Surprising Truth About Inductors: How They Really Work in Circuits

In our last series, we looked at the behavior of solenoid when connected to a DC supply. And hopefully, by now we know that when a DC voltage is applied across a solenoid, the growth of the current through it is not instant but is determined by the self-induced current, or through the back EMF value that is generated by the coil. In today's series, we will be looking at how an inductive coil tends to resist the change in alternating current. So let's get started. Inductor as it is fondly called played a critical part in the design of an electrical circuit. That is because of its ability to store electrical energy via magnetism, unlike a battery cell where electrical power is stored via chemical action, or in a capacitor via electric plates. These simplest forms of storage by an inductor make it possible to be easily integrated into an electrical circuit. Although, the contribution of Michael Faraday and Joseph Henry on electromagnetism can not be overemphasized, which is because Faraday discovered how current is induced via magnetism, while Joseph Henry is attributed to the discovery of self-inductance when he perceives a spark accidentally when breaking a circuit. However, Lenz was credited for revealing that the magnetic field which is generated by the induced current tends to oppose the changes in the initial magnetic field. So in a nutshell, inductor opposes any changes in current through them. This behavior will be practically looked at in a moment. So Lenz discovered that thrusting a pole of a permanent bar magnet through a coil of wire will induce an electric current in the coil. The induced current will in turn set up a magnetic field around the coil. After this demonstration, Lenz was able to have an indication of the direction of the induced current. This law by Emil Lenz, i.e. the direction of the induced current was what contributed to the minus sign in Faraday's law of electromagnetic induction. Of course, in magnets, like poles repel each other. So, Lenz's law states that, when the north pole of the bar magnet is approaching the coil, the induced current flows in such a way as to make the side of the coil nearest the pole of the bar magnet itself a north pole. These like poles will tend to oppose the approaching bar magnet. And upon withdrawing the bar magnet from the coil, the induced current reverses itself, and the nearest side of the coil becomes a south pole to produce an attracting force on the receding bar magnet. So, a small amount of work is needed in pushing the magnet into the coil, and when pulling it out of the coil, in which the south pole tends to prevent the magnets from coming out of the coil. Now, looking at this setup here, we have an inductor coil here which is connected in parallel with the source here, and a bulb is further connected in parallel with the circuits also. However, in order to increase the strength of the magnet, a ferrite rod is inserted within coil. Again, sometimes magnets are also used. Now in order to fully understood how inductor behaved practically within a circuit, when I flipped this switch to the on position, and when we looked at this circuit in a blink, and assuming the sinusoidal current is at its maximum and remain there, electron will flow along the wire leading to the inductor, and a magnetic field is produced around the wire. At this point here, the flowing electron will split in such a way that current will flow to the inductor and the bulb simultaneously. Now, looking at the inductor, the magnetic field flowing along with electron will begin to form a bigger magnetic field within the inductor, and the intensity will begins to grow as the inductor reaches its maximum value. Now, the magnetic value generated within the inductor will be much more stronger than the magnetic field generated along the wire. This where the magnetic effect will be noticed. Although, the current has splits at this point, more current tends to flows to the bulb at the initial stage. This is because of the growing magnetic field of the inductor. And according to Michael Faraday law, it will induce another current which will tends to opposes the change that is now happening within the inductor. That is because, inductor don't like the states of its current to change value. Which is because, back EMF is generated which tends to prevent the change that is happening within the circuit. And as such, more current will be pushed towards the bulb. But this current diversion is brief. Once the generating magnetic field in the inductor reaches its maximum, the current will stop flowing to the bulb, and the bulb will be switched off. That is because, at this point, the inductor will start behaving like a wire with less resistance. So the current will now tends to flow through the inductor back to the source. Which is because, the bulb offers more resistance to the flow of the current than the inductor. Now, when the supply suddenly changes, as in when the current in an alternating current is at minimum. Now, another back EMF will be generated such that it tend to keep the current of the inductor at the current states. As such, we can say that, it opposes the change that created it. Which is because inductor don't like changing current. Hence, the already charged magnetic field will now discharge via the bulb. And as such, the inductor will push electron to the bulb until the magnetic field is completely discharged via the bulb. That is why during circuitry design, in order to protect the circuit from sudden surge, some forms of draining resistive devices are usually connected with the inductor. And it is a result of the practical experiments that we can analyze the circuit in terms of the position of the current with respect to voltage, and the waveform of back EMF. With these, we can be able to study the inductance as related to the rate of the changing voltage using these graphs here. So with an alternating supply, when the flowing current is at maximum, the induced current will be at minimum. And when the self-induced current is at maximum, the flowing current will be at minimum. Again, because the EMF is proportional to the induced current. So when the EMF is at maximum, the induced current will also be at minimum. And verse versa. These voltage and current waveforms show that for a purely inductive circuit, the current lags the voltage by 90 degrees. This can also be expressed mathematically as this, where the inductive voltage is equal to zero degrees, and the inductive current is equal to minus 90 degrees with respect to the inductive voltage. If the voltage waveform is classified as a sine wave, then the inductive current can be classified as a negative cosine, and the value of the current at any point in time can be expressed mathematically like this, where the angular frequency is in radians per second, and t is in seconds. Since the current always lags the voltage by 90 degrees in a purely inductive circuit, we can find the phase of the current by knowing the phase of the voltage and vice versa. So if we know the value of inductance voltage, then the inductance current must lag by 90 degrees. Likewise, if we know the value of inductance current, the inductance voltage must therefore lead by 90 degrees. Then this ratio of voltage to current in an inductive circuit will produce a mathematical equation which is expressed as this, and which define the inductive reactance of the coil. Now, that mathematical equation can be rewritten into a more familiar form that uses the ordinary frequency of the supply instead of the angular frequency in radians. This will now be expressed mathematically as this, where f is the frequency, and l is the inductance of the coil. Again we know that, 2 pi f is equal to the angular frequency. From these mathematical expressions, as in inductive reactance, it can be seen that if either of the frequency or inductance was increased, the overall inductive reactance value would also increase. As the frequency approaches infinity, the inductive reactance would also increase to infinity. This will make the inductor to act like an open circuit. However, as the frequency approaches zero or DC, the inductive reactance decreases to zero, which means, the inductor here also acts like a short circuit. So from this behavioral pattern, it means that, the inductive reactance is proportional to the frequency. In other words, inductive reactance increases with frequency resulting in inductive reactance being small at low frequencies and, inductive reactance being high at high frequencies. And this can be seen in this graph here. In choosing an inductor, there are different parameters to consider when choosing them. These are, the DC resistance, self resonant frequency, and the Q factor. The DC resistance is usually measured in ohms. So a higher DCR means more power will be lost due to the heat generated through the coil. And a low DCR results in more efficient power supply. Self-resonant frequency on the other hand is the frequency at which the inductor filters best. So when above the self-resonant frequency, the inductor's ability to block noise decreases. Therefore in an ideal setting, the self-resonant frequency should be much higher than the operating frequency. The Q factor is the ratio of inductance to resistance at a given frequency. The higher the Q factor, the closer the inductor is to an ideal inductor. So we can calculate the current that will flow in this circuit here using the value of components that is present within this setup here. The inductance is 120 mH, and zero resistance is connected across a 240 V, with 50 Hz power supply. With these parameters here, the inductive reactance will be 37.68 ohms, while the current flowing through the circuit will be 6.37 ampere. And it is on that note that there are four types of inductors. These are EMI filters, RF inductors, power inductors, and transformers, which can also be known as coupled inductors. EMI filters are used to reduce electromagnetic interference. RF inductors are usually used in wireless communication applications. This is due to their ability to be optimized for the highest signal integrity. Power inductors are used in power packs for power protection against current surges, and to provide smooth power output. Transformers or coupled inductors are used to step up or step down the voltage in a circuit, and to provide isolation. With these, we have come to the end of today's series. I hope you have learned something new today. See you at the next one.