In an inductor, when transient state is considered, the current will increase gradually as the inductor opposes the change in the current. But for deep understanding, let's have a look at newton's first law of motion..
“Every object in rest or motion tends to remain in its state unless its disturbed by external forces”
Now, initially, the inductor was idle but we tend to pass current through it. The inductor hates it. It tries to produce current in opposing direction so that it can cancel out the entering current so that it can remain in idle state. This is what we call as self inductance. The ability of an inductor to oppose the flow of current through itself..
But wait.. Where does the inductor get the source of opposing current it had produced? Doesn't it oppose law of conservation of energy?
No. We know that changing magnetic field can produce a current. So the source of opposing current is just the increasing magnetic field produced when the current increases gradually through the inductor. Hence, once steady state is reached, no opposing current is produced as the magnetic field becomes constant and only changing magnetic field with respect to time can produce a current..
So, the self inductance plays a role only in transient state.
Now, energy stored in the inductor means that it can produce the current even after the source is switched off. The energy here means the one used to pull the electrons and now you could have understood why it is referred to as “energy is stored in the inductor in the form of magnetic field”.
Let us move to capacitors. These are simpler than inductors.
We all know that capacitors are simply two metal plates separated by a distance with dielectric material in between them to increase capacitance. When negative potential is given to one plate and positive to another plate, the electrons accumulate on the negative plate of the capacitor as much as it can(determined by the capacitance value) provided that it is connected for sufficient time. When the source is switched off, the electrons accumulated there finds some other way through circuit to reach the positive plate of the other end in order to neutralize the charges. Hence “energy stored” here is taking advantage of the fact that electrons are attracted towards positive potential. So now its clear that “energy is stored in a capacitor in the form of electric field”.
Charges through inductor produces magnetic field and in capacitor produces electric field.
In case of Resistors:
Resistors are like a block to the flow of charges, and hence charges should spend some energy to cross them. And that energy is dissipated as heat in the resistor.
Hell yeah, charges through resistors produce heat.
But the problem here is, change in heat won't produce any energy to move the charges.. It just goes away ad heat.. Nothing else.
There may be a solution. But till now, scientists haven't discovered any method to make energy from the heat which is dissipating on the resistor.
So now, the problem is moving charges through resistor produces heat. So it can't store any energy.
