# Inductance -- why does current lag voltage?

• derek181
In summary, when discussing the lag between current and voltage in an inductive circuit, it is important to understand the underlying principles of electromagnetism. The equation E=ldi/dt can provide an explanation, but on a molecular level, the concept becomes more complex. The lag can also be understood through the concept of energy storage in capacitors and inductors, and the time it takes for energy to be transferred between them. Additionally, the shape of the current waveform can affect the shape of the voltage waveform in an inductor.

#### derek181

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?

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. . . .

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.

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

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.

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.

sophiecentaur said:
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 ;-(

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

derek181 said:
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.

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.

An inductor is just a short circuit to a non changing current. There will be no Volts across it when DC passes. When you change the current, the magnetic field will change and induce a Voltage in the wire (by Lenz's Law, it will be in opposition to its cause), The faster the current changes, the greater the voltage so the peak of the voltage when an Alternating Current happens to be sinusoidal, will be as the current waveform changes at its fastest rate i.e. at the zero crossing.
Note that when the current waveform is not a sinusoid, the Voltage waveform will be a distorted version of the waveform because each frequency component is shifted by 900, which will not produce the same shaped resultant waveform. So you will not just get a time shifted version.

## What is inductance?

Inductance is a property of an electrical circuit that causes it to resist changes in current. It is measured in units called Henrys (H) and is represented by the symbol L.

## How is inductance related to current and voltage?

When there is a change in the current flowing through an inductor, a voltage is induced across it. This is known as self-inductance. The induced voltage opposes the change in current, causing it to lag behind the voltage. This is why current lags voltage in an inductive circuit.

## Why does current lag voltage in an inductive circuit?

In an inductive circuit, the time-varying magnetic field created by the changing current induces a voltage across the inductor. This induced voltage opposes the change in current, resulting in the current lagging behind the voltage. This effect is known as inductive reactance.

## How does inductance affect the behavior of an electrical circuit?

Inductance plays a crucial role in the behavior of electrical circuits. It causes the current to lag behind the voltage in an inductive circuit, which can affect the power and efficiency of the circuit. It also causes the circuit to resist changes in current, leading to the storage of energy in the magnetic field of the inductor.

## How can inductance be calculated and controlled in a circuit?

The inductance of a circuit can be calculated using the formula L = NΦ/I, where N is the number of turns in the inductor, Φ is the magnetic flux, and I is the current. To control inductance, different types of inductors and materials can be used, and the number of turns can be adjusted. Additionally, inductive components such as capacitors can be used to cancel out the effects of inductance in a circuit.