# Inductance -- why does current lag voltage?

## Main Question or Discussion Point

Could someone give me an intuitive explanation as to why the current lags the voltage in an inductive circuit. I can understand it through the equation E=ldi/dt. But how exactly does the current lag, on a molecular level?

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sophiecentaur
Gold Member
EM effects are not "molecular" phenomena so I don't think there exists an answer on those terms. But you could perhaps think of how the emf that is induced across an inductor will be proportional to the rate of change of the magnetic field i.e the current flowing. If the current is sinusoidal then the voltage will have the biggest value when the current waveform passes through zero.
The Mathematical description takes a lot of beating - horses for courses. . . .

CWatters
Homework Helper
Gold Member
Perhaps start by understanding why voltage lags current in a capacitor. When you turn on the current, charge flows into the capacitor and the voltage builds up much like water filling a bucket. You don't expect a bucket to fill up the instant you start pouring in water.

Inductors are essentially the compliment of a capacitor.

sophiecentaur
Gold Member
What a perfectly splendid Capacitor you have there. :D
It complements the colours on your resistor stripes well.

Khashishi
In a typical conductor, electrons carry the current. Current is just the flow of electrons. A voltage is an electric potential, which is generated by an imbalance of charge. The electric field is just the spatial derivative of the potential, ##E = -\nabla \phi##.

You can break it down into simple Newtonian mechanics. The electric field exerts a force on electrons, which accelerates them. Therefore, the electric field causes a current to form, and the current lags behind the electric field (and voltage) due to the inertia of the electrons.

sophiecentaur
Gold Member
It isn't simple Newtonian mechanics; that's far too simplistic to be of use in understanding what is happening in an inductor. The electrons have such little mass and the KE involved is so low that it plays no significant part in the way circuits work. The macroscopic approach is more than enough to account for what is measured.

CWatters
Homework Helper
Gold Member
What a perfectly splendid Capacitor you have there. :D
It complements the colours on your resistor stripes well.
My spelling is even better than my dress sense ;-(

sophiecentaur
Gold Member
It did make me smile. Only a temporary lapse on your part, I'm sure. :)

Could someone give me an intuitive explanation as to why the current lags the voltage in an inductive circuit. I can understand it through the equation E=ldi/dt. But how exactly does the current lag, on a molecular level?
I cannot explain in molecular level, but I hope a physical explanation should suffice.
Lets say, you apply a voltage = E, across an inductor (which is actually just a coil of wires). Now, since an inductor is actually just wires wound into coil, current will tend to flow. But, the current cannot suddenly rise, because, the change in current would create a changing magnetic field (remember it is a coil), and that changing magnetic field would produce/induce an Emf in the coil, that opposes the applied emf. If the current tends to change too fast, the internal emf will tend to exceed the applied emf, and hence the current will have to reduce. If the current doesn't change fast enough, the applied emf will increase the current and make it change quick. So, only allowed case is if the current change just in the right way. For an inductor with zero resistance, the E_applied = E_internal must be instantaneously be true, otherwise the difference would create infinite current. If you assume the initial condition to be I=0 and E_internal = 0 and apply the E_applied, then I will increase instantly (and would tend to be infinite), but to do that it will need to change, and the change will make E_internal = dI/dt. So, it can neither change faster than dI/dt = E_applied nor can it change slower than that. So, for +ve E_applied current will increase and for -ve E_applied current will decrease, which makes the current tend to follow E.
Having written all that, I think, it doesn't do better than just saying "its because the inductor follows that equation, and the solution of that equation implies that current lags behind voltage", and which doesn't really answer your question. But anyway, I tried.

CWatters
Homework Helper
Gold Member
The energy stored in a capacitor is proportional to the charge in the capacitor and hence the voltage.
The energy stored in an inductor is proportional to the magnetic field and hence the current.

It takes time to move energy from one place to another so it takes time to move energy into or out of a capacitor or inductor.

So..
In a capacitor it takes time for the voltage to build up following a step change in the current.
In an inductor it takes time to for the current to build up following a step change in the voltage.

In both cases it's the fact that it takes time to move energy is the cause of the lag.

sophiecentaur