Why does the inductor discharges in the same path ( same direction of current ) as that of its charging unlike a capacitor which discharges in the direction opposite to its charging(current direction is reversed in discharging).?
What could be its physical reason (for Lenz's Law)
[Physics] Inductor Charging and Discharging
electricityelectromagnetismelectrostaticsexperimental-physics
Related Solutions
My question is why does that emf cause a decrease in the rate of change of current through the inductor
The emf doesn't 'cause' a change in the rate of change of inductor current but it is, however, consistent with the rate of change in inductor current.
The fact is that the rate of change of current, the associated rate of change of magnetic field, and the associated non-conservative electric field must satisfy Maxwell's equations (the governing equations of classical electromagnetism) at each instant of time.
For the case that there is a constant, non-zero voltage across the inductor, Maxwell's equations are satisfied when
- the inductor current changes at a constant, non-zero rate
- the magnetic field changes at a constant rate, non-zero rate
- the non-conservative electric field is constant and non-zero (which implies a constant, non-zero emf).
So it isn't true that the emf causes a change in rate of change of inductor current since, as pointed out above, there is a perfectly consistent solution in which the emf is non-zero and the rate of change of current is constant.
Wouldn't this inductor's emf counteract the discharging capacitor and actually charge it? / stop the capacitor from fully discharging?
The inductor doesn't care about what the charge state of the capacitor is. All it cares about is how quickly the current through it is changing, and it generates a back-voltage according to the equation V=L*dI/dt. You can think of an inductor as giving "momentum" to the current. If the current is zero, then it wants to keep the current zero. If the current is non-zero, it wants to keep the current at that same non-zero value. If the current is increasing, it generates a counter-voltage acting in the opposite direction to the current flow.
The analogy I like to use is a circuit of water pipes in which inductors are represented by a heavy propellor in a water pipe. If water flow is suddenly turned on, the heavy propellor initially resists the flow of water. But over time the propellor spins faster in response to the water flow. If the water flow past the propellor is then reduced, the heavy propellor resists the decrease in water flow because it is now spinning fast and tries to continue pushing the water through the pipe. This is analogous to how an inductor resists changes in the electrical current flow through it.
Using this water circuit analogy, a capacitor can be represented as a section of pipe which has a rubber membrane stretched across the inside of it. If you push water into one end of this pipe section, the rubber membrane stretches and creates a back pressure resisting attempts to push more and more water into it. If you then stop applying water pressure to that side of the pipe section, the rubber membrane springs back to its flat, equilibrium position, pushing the water back out the same side of the pipe as you were trying to push the water in. This is analogous to how a capacitor "pushes back" with a back-voltage when you push electrical charge into a capacitor.
If you make a closed electrical circuit with this heavy propellor (which represents the inductor) and the rubber-membrane pipe section (which represents the capacitor), then you should be able to see how a resonant water oscillation in the circuit can be set up. Imagine the rubber membrane pipe section being "charged" by forcing water into one side. When you release the applied pressure, water will flow past the heavy propellor, which will then speed up and try to maintain a constant water flow past it. However, as the water flows past the heavy propellor and into the other side of the rubber membrane pipe section, the rubber membrane goes to its equilibrium position and then starts getting stretched in the opposite direction. Eventually, the back-pressure becomes so large that the direction of water flow is reversed and the cycle happens all over again.
In summary, with this analogy we have the following:
electrical current <-> water flow
voltage <-> water pressure
inductor <-> heavy propellor
capacitor <-> rubber membrane pipe section
Hopefully, visualizing things this way can give you an intuitive grasp of how a capacitor and inductor work together to form a resonant circuit.
Best Answer
For a capacitor, the voltage across must be continuous since the current through since
$$i_C = C \frac{dv_C}{dt}$$
Since the current through is proportional to the time derivative of the voltage across, the $v_C(t)$ must be differentiable, i.e., there can be no discontinuous change.
There is no such limitation on the capacitor current, the direction and/or magnitude can be discontinuous.
The inductor is the electrical dual to the capacitor so we have
$$v_L = L \frac{di_L}{dt}$$
and thus, the inductor current must be continuous and so, the current cannot discontinuously change. Instead, the slope of the current changes discontinuously from increasing (the inductor is 'charging') to decreasing (the inductor is 'discharging') and the voltage across instantaneously changes sign and possibly magnitude.
The physical reason is Faraday's law of induction. Since the magnetic flux threading the inductor is proportional to the inductor current, an abrupt change in current implies an abrupt change in magnetic flux which, by Faraday's law implies an 'infinite' (arbitrarily large) emf.