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yes..only the application is different.
voltage across inductor create a flux. because of variation current developes an opposite emf.
An inductor resists a change in current. The equation is ... di/dt = V/L ... where di/dt is the rate of change of current in amperes per second, V is the EMF is volts, and L is the inductance in henrys. Looking at this, you can see that the slope of the current is proportional to the voltage and inversely proportional to the inductance. One characteristic of inductors is that when you have a current established, and then break the circuit, the inductor will respond by trying to maintain the current. If this is not possible, such as when the circuit is open, the inductor will generate a large reverse EMF - in the theoretical case, an infinite EMF - in the practical case, several thousand volts, depending on the inductor. This is why proper design of inductors in DC circuits, such as relays and solenoids, must include reverse EMF suppression, such as a diode or resistor across the inductor.
The fluctuation of the AC which sets up an magnetic field and causes a reverse emf is lost with DC because there is no variation in the field.
The emf of a batter as it is used will stay the same.
Yes, an inductor allows DC to pass through it. An inductor resists a change in current, proportional to inductance and voltage. At equilibirum, an ideal inductor has zero impedance. The differential equation for an inductor is di/dt = v / l
No
How do you propose to connect a decreasing current to the inductor ? The initial current through the inductor is zero, and you want to connect it to a current which is not zero and decreasing. At the instant you make the connection, the inductor current is zero, and it must rise to the non-zero value where you want it to begin decreasing. The current in the inductor cannot change from zero to something in zero time. As it rises from zero to the initial value, guess what . . . the inductor is storing energy in its magnetic field, while producing the usual voltage equal to [ L di/dt ].
There is analogy between pressure and EMF or voltage. What pressure is to the liquids, EMF or voltage is to electric current. But, of course, they are not the same.
Since the equation of an inductor is ... di/dt = v/L ... then increasing the current in the RL network would cause a back-emf in the inductor that would initially seem to oppose the series current. More correctly, the question should ask "what if the voltage were increased?"; and the answer is that the rate of change of current in the inductor would increase, but the current would not initially change. This is the case for a series RL. For a parallel RL, increasing the current would initially show up as an increase the the current through the R, increasing voltage in the L, with the same effect as noted above.
Transformers depend on fluctuating magnetic fields in order to operate. The operating principle of an inductor, of which a transformer is an example, is to resist a change in current by back EMF which bucks the change (up or down) in current. If you place DC across an inductor, the current would linearly increase until the resistive limit is reached, the power supply's capacity is reached, and/or the inductor self destructs from overcurrent.
The physical interpretation of voltage leading current (by 90o) in an inductor is just that. The instant voltage is applied, the inductor "feels" the applied voltage and responds by "beginning to generate" a reverse voltage (reverse electromotive force or emf, or back emf) which prevents current from flowing for the first instant of time. At time zero, the inductor is infinitely resistive. As time goes on, current is increasing. It is trying to "catch up" to voltage, which is continuing to climb. The back emf is trying to limit current, but it climbs to try to "follow" the increasing voltage. But voltage peaks and starts down. The magnetic field that was building while voltage was climbing (and was "holding back" current flow at the same time) will begin to collapse. The collapsing field generates emf that will try to keep current flowing, so current will continue to increase while voltage is decreasing. The current peaks later on (like 90o later) and then starts to decrease. In a purely inductive circuit to which AC is applied, the current is "chasing" the voltage peaks and is always 90o degrees behind. [There are other ways to look at the situation, but this one is a basic way to interpret the physics.]