So far, we’ve talked about electricity and capacitors. This time we’ll be addressing inductors. Why am I doing this? …explaining these electric circuitry, current and horror stuff? Well, a friend of mine, asked me to write posts on these basic circuit components intuitively. While acquiring intuition is totally up to you (based on your interest, curiosity, how well you grasp things, etc.), I can guarantee you for sure, that I’ll be sticking to my motto, the Occam’s Razor. Mostly, I’ll try to explain things simply. But, when I fear that treating some complex stuff “simply”, may drive people into some misconception, I’ll start including the required complexity step-by-step. Anyways, you don’t have to worry about that. You have the space for comments (shoot me with your questions, wherever you get “stuck”). Just keep up with the hope that it’ll be easy…

Our topic requires introduction to the magnetism. I shouldn’t be writing historical things. But, I can’t resist myself from speaking about Faraday, the one who knew how much a current can do, who observed all those mysteries, before Maxwell (who did the unification and gave “light”). He didn’t need a giant laboratory for his fun. His “CERN” was able to fit to his bench, where he played with his little coil of wires and magnets with the newly discovered electricity. Then, the shocking moment arrived. He observed that when a magnet is moved towards a coil of wire, the galvanometer showed deflection indicating the flow of current. The thing is, the current lasted only as long as he moved the magnet. It stopped when he stops his motion. He also discovered that when an electric pulse is sent through a wire, a magnetic needle (compass) showed deflection (deviation from its pointing to “North”, to some direction around the wire) indicating that there’s a magnet in the wire when current flows through it.

He was curious about his discovery that forms a new bridge between electricity and magnetism. He just can’t understand what exactly is the underlying clockworks. Anyone may wonder when they come to know that the stuff that lights the streets has something to do with the things that stick to metals here and there. But, he tried to understand the magnetic field by visualizing in terms of some lines, what he called the “flux lines”. The current-carrying wires (the magnets too) emit some kind of field lines where the compass needle or any other magnet gets a force. Shown below, is the analogy for field lines (the experiment was actually devised by Oersted in the 18th century)…

## The “laws” of induction…

Using these lines, he devised two laws (which we now call the laws of electromagnetic induction). Whenever the number of magnetic field lines crossing the coil’s area (called the flux $\phi$) changes, a voltage is induced which lasts as long as the “number of lines crossing the coil’s area” changes. He added that this voltage also depends on the rate of change of the flux (i.e) more voltage is induced when there’s a miraculous change in the number of lines passing through the coil, within a specific time interval. Mathematically, it’s represented as…

$V\propto$ $\frac{d\phi}{dt}$

A few years later, Lenz corrected his law that the voltage produced in the coil always acted in a way that it opposes the cause that produced it (i.e) the current flow (generated by induction) creates its own magnetic field that opposed the moving magnet’s field. What does it mean? When you move the magnet towards the coil, the coil resists the motion of magnet by repelling it and when you move the magnet away from the coil, it resists the motion again by attracting the magnet. It was also found that the voltage induced depends on the turns of the coil (say $N$). The more you wind the coil, the larger the induced voltage. Now, the corrected form would be (having found the proportionality constants)…

$V=-N$ $\frac{d\phi}{dt}$

While these laws don’t tell anything about how exactly this kind of horror works, instead they just say “what would happen” when you do such an experiment. This is more than enough for us today.

## Now, to our inductor…

An inductor is just a coil with some turns, the same what’s been used by Faraday. What happens when current “starts” to flow through such a coil? Well, it becomes an electromagnet, which we know. But, that’s not what we want here. Lenz has done the job for us. He has inferred that the current through the coil opposes the change or cause that produces it. Say you’re providing a power supply to the inductor. Instead of increasing straightaway, the current (or voltage) increases linearly with time (i.e) there’s a time-varying magnetic field in the inductor. As the current reaches a certain value, say 2 amperes, a magnetic field corresponding to that current is produced which opposes the further growth of current. It won’t be a trouble to think that the now-produced magnetic field generates its own emf (a fancy name would be the “back emf”) that opposes the applied voltage.

The more the current grows, the more the corresponding magnetic field intensity grows, which further delays the growth of current. Thus, the maximum value of current is attained in this kind of linear variation (much like a step-by-step manner), and once it’s established, the current simply flows through the inductor without any resistance due to magnetic field. Now, the same happens when current decreases. When the current decays from its value, the magnetic field opposes its decay. Again, a linear time-dependent variation is seen. In much simpler words, the inductor resists current flow as long as there’s a change in the applied voltage.

## Demonstration with a light bulb…

The last few “sayings” might have confused you. Let’s go with an experiment. What do you see in the following circuit? It’s a parallel circuit of an inductor and a light bulb, connected to a battery (DC). This circuit is just a rough sketch. You can’t see what’s really going on because you’d need a moving picture for that (creating such things is something I’m not too much inclined to). Okay…

The moment you close the circuit, current starts to flow. Common sense might suggest that larger current follows a path of relatively least resistance. The inductor seems to support that statement. So, the bulb should appear dim. That doesn’t happen. So, what exactly does happen? When you close the circuit, the bulb glows brightly and dims out soon.

Always keep in mind that the inductor has a self inductance (just a fancy way to call its property) that makes it oppose the applied voltage with its own magnetic field (which has also just been generated by the applied voltage). So, the instant you close the circuit, there’s a large potential difference and thus, the inductor acts as if it were showing a great resistance to the current flow. Now, bring back your suggestion. Most of the current flows through the bulb that makes it glow brighter. Once the current reaches its maximum value, there’s no change in the voltage and so, the inductor stops opposing via its magnetic field. This results in current flow through the inductor and as a result, the bulb becomes dim.

One more thing should be noted here. When you break the circuit open, the current starts to decay and now, the inductor’s magnetic field opposes the decay of current. This current passes through the bulb, that makes it glow brighter and die out eventually.

## In AC & DC circuits…

The inductor opposes only when there’s a change in the voltage (or current). Hence, the inductor offers high resistance to AC (oscillating around like mad) depending on its frequency, whereas DC doesn’t experience any issues with the inductor. It’s just another piece of wounded wire. The resistance (formally called the impedance) is zero doesn’t mean that the inductor is superconducting. Just because there’s no change happening in DC (except at the start), the magnetic field doesn’t oppose the current, during the whole business. But still, there’s the ohmic resistance that depends on the wire, which leads to dissipation in the form of heat.

We’ve finally concluded that the inductor stores electromagnetic energy unlike capacitor (where the thing is electrostatic). Now, to our phase diagram. The amplitude is less since there’s always an ohmic resistance offered by the inductor. Then, there’s the phase shift that the voltage overtakes the current by a phase angle of $\pi/2$.

Keep in mind that the voltage dropped across the inductor is the effect against the change in current that passed through it (i.e) it takes some time for the voltage to build up the current to its maximum value due to the presence of this Lenz law horror, which opposes the growth of current. So, the instantaneous voltage is zero, whenever the instantaneous current reaches peak value (where the slope, the change is zero) which implies the phase shift…

(Again) In order to get a good understanding of these sloppy things, you should try reading the hydraulic analogy. You can get over with it. I’m not going into it, as I don’t think I might be a good competent for Wikipedia.