# Inductors in an AC circuit

I have read that inductors oppose change in current flowing in the ac circuit. For example, when current starts increasing it induces an emf in the opposite direction to oppose the current from rising. Now I have two doubts concerning this.

Firstly, when an inductor opposes the current from rising still the current rises although less steeply, why is it so?

Secondly, we know the inductor induces an emf but between which two point does this voltage exist?

Firstly,when inductor opposes the current from rising still the current rises although less steeply,why is it so?

I think that part of your confusion is that the statement "an inductor opposes a change in current" is hopelessly vague. What does it mean for an inductor to "oppose" something? When I oppose something I generally vote for the other candidate. So does an inductor write anti-current-change posts on its favorite social media site and vote for the pro-static-current candidate? Of course not.

The correct description is $$v=L\frac{dI}{dt}$$ meaning that the voltage across an inductor is proportional to the change in current through the inductor. I have no idea how "voltage is proportional to" was ever translated to "opposes", so I prefer to use the clear phrase "voltage is proportional to" instead of the ambiguous phrase "opposes" even though it is a few more words.

So, with better wording, it is clear that the current changes because there is a voltage across the inductor and by definition the voltage across an inductor is proportional to the change in the current through the inductor.

Secondly, we know the inductor induces an emf but between which two point does this voltage exist?

The voltage across the inductor is measured at the terminals of the inductor. Ideally, the magnetic field should be entirely contained within the inductor and should not leak outside of the inductor so that even though the voltage is caused by a non-conservative E-field inside the inductor from the terminals it behaves as any other circuit voltage.

• Just to be clear, are you saying an inductor does not oppose a change in current? – Bob D Jan 10 '20 at 23:55
• I am saying that it is hard to know what “oppose” means in this context. I think it is a confusing word to use here. So I recommend using the more accurate wording instead. An inductor’s voltage is proportional to its current. That is accurate, clear, and complete. – Dale Jan 11 '20 at 1:16
• @Bob D I know you wanted me to be clear, but I just don’t know how I can take a clear stand on unclear terminology. – Dale Jan 11 '20 at 1:22

Firstly,when inductor opposes the current from rising still the current rises although less steeply,why is it so?

The inductor doesn't oppose current, it induces a voltage that opposes the rate of change in current.

The relationship between the current in and voltage across an inductor is given by

$$v(t)=L\frac{di(t)}{dt}$$

From the equation you see that the greater the rate of change in current, the greater the induced voltage that opposes that change.

See diagrams below. Let's say the current is the sine wave, then the induced voltage is the cosine. Note at time = 0 the value of the cosine is maximum in opposition to the supply voltage when the sine is zero but its rate of change (slope) is maximum positive, meaning the induced voltage opposes the change in current. As the slope of the sine decreases (i.e., its rate of change decreases) the induced voltage decreases in opposition to the supply voltage.

Secondly, we know the inductor induces an emf but between which two point does this voltage exist?

The emf is across the ends of the inductor as shown in the diagram.

given this opposition in change of current from inductor why the current still manages to change?

Because an inductor resists a change in current, it does not prevent it.

An inductor with a constant current produces a magnetic field. That magnetic field represents stored energy in the inductor, in this case, in the form of kinetic energy. (A capacitor has stored energy in the electric field between the plates and, in that case, the stored energy is electrical potential energy). Perhaps the following mechanical analogy will help.

Now think of a mass moving at constant velocity and having kinetic energy. It will resist any attempt to slow it down (reduce its kinetic energy) or speed it up (increase its kinetic energy) analogous to an inductor resisting any attempt to change its current (and thereby changing the kinetic energy of its magnetic field). The mass has inertia. The inertia (to current change) of an inductor is analogous to the inertia (to velocity change) of the mass. The analogy can be seen when one compares faradays law of induction.

$$v(t)=L\frac{di(t)}{dt}$$

With Newtons's second law of motion

$$F=M\frac{dv(t)}{dt}$$

Very roughly speaking, we can consider:

1. Voltage as the analogue of force
2. Inductance as the analogue of mass
3. Velocity as the analogue of current.

I would like to stress that inductance is not mass, velocity is not current, and voltage is not current. The analogy is simply intended to help you get some feel as to what is going on.

Hope it helps

• given this opposition in change of current from inductor why the current still manages to change? – Sharad Jan 10 '20 at 15:40
• Because most the time, the induced voltage is not sufficient to balance out the change in current. – Sam Jan 10 '20 at 17:20
• @Sharad because an inductor resists a change in current not prevent it. The mechanical analog of inductance is inertia of mass. The inertia of mass resists a change in velocity but doesn’t prevent it. It changes if subjected to a net force. Does that help? – Bob D Jan 10 '20 at 19:06
• @Sharad I have included the mechanical analogy in my answer. Perhaps it will help; – Bob D Jan 10 '20 at 19:52