This means that the rate of change of current keeps on decreasing as
the time passes. It seems to me as the Inductor opposes the rate of
change of current.However I am not sure.
The inductor does oppose a rate of change in current.
Consider the mechanical analogy of mass and inertia in which the inductance of an inductor is analogous to mass, and the current in the inductor is analogous to the velocity of the mass. The analogy is not exact, but it may hopefully give you a physical "feel" for what's going on.
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 either decrease or increase its current and its stored kinetic energy. 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.
$$V_{L}(t)=L\frac{dI(t)}{dt}$$
to Newtons's second law of motion
$$F=M\frac{dv(t)}{dt}$$
Very roughly speaking, we can consider:
- Voltage as the analogue of force
- Inductance as the analogue of mass
- Velocity as the analogue of current.
The diagram below shows other mechanical analogues for resistance and capacitance.
I am unable to develop an intuition as to why the rate of increase of
current keeps on decreasing. Please provide necessary arguments.
There are only three possibilities:
- The rate of increase in current is increasing (accelerating)
- The rate of increase in current is constant
- The rate of increase in current is decreasing (decelerating)
Only the third possibility can result in the current eventually becoming constant and equal to $V_{supply}/R$ and result in the induced emf of the inductor eventually becoming zero because there is no longer a change in magnetic flux. These are illustrated in the second diagram below.
The other two possibilities result in infinite current as $t$ goes to ∞. You know that can't happen since there is only one independent source of energy (the battery) and one resistor (assuming an ideal (no resistance) inductor) which has to ultimately limit the current to $I=V_{supply}/R$.
Bottom Line: If there were no inductor in the circuit, the current would be a step function, that is, it would theoretically instantaneously rise from zero to $V_{source}/R$ in the bottom diagram. However, since the inductor resists a change in current it effectively "bends" the current vs time function, i.e., decreases the rate of rise, as shown in the bottom diagram.
Hope this helps
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/6MYGo.jpg)
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/0TV5r.jpg)