# How does inductor resist the increasing dc current?

I understand the point that inductor will have high resistance for ac current.this is because the magnetic field produced during positive half cycle will oppose the negative half cycle since the energy during positive half cycle will be stored in magnetic field. But how would this happen there is an increase in dc current.please explain how would inductor react.

• There are only 2 reactive components, capacitors using dielectrics which resist but accumulate charged voltages with current applied ( we call it negative reactive impedance) and (2) inductors using insulated conductors which resist induced current flow and accumulate current charge flow rate with voltage. ( we call this positive reactive impedance). The accumulation is a time integral but with sinewaves it is shown as a phase shift of 90 degrees for V vs I. inductors lag current so I is -90 deg. – Tony Stewart Sunnyskyguy EE75 Mar 1 '17 at 16:55
• With a magnetic field, and if its increasing DC current, its not DC anymore, its 'AC'. – Voltage Spike Mar 1 '17 at 18:21
• @laptop2d the A in AC stands for Alternating. You can have a varying current that is not alternating at all. Exponential, for example. – Sredni Vashtar Mar 1 '17 at 18:29
• I said 'AC' not AC, let me define it: everything above 1Hz. If its a moving signal it has frequency content. – Voltage Spike Mar 1 '17 at 18:50
• A custom vocabulary is in general a 'bad' idea. Besides, when you say "1 Hz" you are implying a periodic signal. Exponential signals are not periodic unless you want to introduce an infinite period. In which case even DC classifies as 'periodic'. :-) – Sredni Vashtar Mar 1 '17 at 21:42

You said it in your question: "an increase in DC current". Sometimes people get all bundled up in the term "AC". AC describes a special kind of changing current which is sinusoidal. We know pretty much everything there is to know about sinusoids, so describing the nature of AC is pretty easy.

An increase in DC current is still a changing current just like the current changes in an AC signal. The same magnetic effects apply (per your question) when there is any type of change in current. It just so happens that AC is a special type of changing current.

Having said that, describing the true conditions of the inductor and its related fields under arbitrarily changing currents requires more general use of electrodynamics laws.

If you want some more elaboration, please speak up. We'll talk about frequency and the Fourier representation of signals to go in a little deeper.

• So i can kinda say that its like the inertia? It opposes the change. – user133933 Mar 1 '17 at 16:34
• Kinda? Yes. You could say you have to 'push' space into the magnetic field configuration that goes with the current. – peter Mar 1 '17 at 16:38
• It's kind of like inertia but definitely more complex. Sometimes using more classically mechanical terms to describe electromagnetics can be useful but sometimes misleading. – Envidia Mar 1 '17 at 16:39
• Actually, there is a well established electrical to mechanical analogy and inductance corresponds to mass. Not more complex: same equation. – Sredni Vashtar Mar 1 '17 at 18:22
• @Sredni Vashtar That comment was definitely more opinionated. While there are definitely direct mechanical analogies to electrodynamic expressions, it is my stubborn belief that relying on them is an easy way to miss caveats inherent with electromagnetism. – Envidia Mar 1 '17 at 19:51

But how would this happen there is an increase in dc current.please explain how would inductor react.

In order for the current through the inductor to increase, the magnetic field in the core has to increase. This means the stored magnetic energy has to increase.

The magnetic energy can only increase as fast as the applied electric power allows. For example, if you want 1 more joule of magnetic energy, you must supply 1 watt for 1 second, or 2 W for 0.5 s...some combination that adds up to 1 J.

The net result of this requirement is the usual relationship that defines an [ideal] inductor

$$\frac{\rm{d}i}{\rm{d}t}=\frac{v}{L}$$

The inductor will react the same for AC and DC. The energy stored in an inductor is $$E_L = {1\over 2} L \cdot i(t)^2$$ and in a capacitor $$E_C = {1\over 2} C \cdot v(t)^2.$$ The energy depends on the instantaneous current or voltage, AC or DC.

To change the energy or current, the voltage $$v(t) = L {d i(t) \over dt}$$ is required on the inductor.

For a capacitor the current required is $$i(t) = C {d v(t) \over dt}.$$

The magnetic or electric field takes time to change and the size of $L$ or $C$ is what resists the change.

I the inductor is designed for AC, and then used in DC, it might saturate, causing the inductance to become almost the same as for a free-air winding.

Tell me if I need to simplify this a lot and I will try.

the magnetic field produced during positive half cycle will oppose the negative half cycle since the energy during positive half cycle will be stored in magnetic field.

You are misunderstanding how this works. The inductor doesn't "wait" for the negative cycle before opposing a change. It's doing it the whole time. At the beginning of the positive cycle, it is opposing the rise in current as it builds to the peak. As the positive cycle begins to return to zero, it opposes that, too (it wants to push it, so it doesn't decrease). The same thing is happening on the negative part of the cycle. As you pass through zero, the inductor is still trying to push current forward (using the residual field), but as the applied voltage is now going negative, the forward push is still in opposition. And so on.

In a "dc" circuit, the moment the voltage changes (and the current tries to change), the inductor opposes it. The inductor doesn't know if this change is the start of an AC cycle, or a change in the DC voltage. And if I were to clip out this very tiny part of the waveform and show it to you, you couldn't tell, either.