# Inductance and the current through the inductor

I am a high school student studying inductance, there is some point I can not wrap my head around, my teacher said that if we closed an LR circuit , at t= 0 the current in the circuit is zero and this is just because the back emf that the inductor generated due to the change in magnetic flux and this emf is equal to the electromotive force supplied by the battery, but I really doubt that,I mean if the inductor was capable of creating a back-emf equal to the electromotive force once the LR circuit was closed ,it will always create the same opposing emf to the electromotive force at any point of time based on the logic that the inductor was just fighting the change in magnetic flux through it, the second argument I have is that there was just no change in magnetic flux in the inductor once the circuit was closed, I mean if the current was zero amps how on earth can the magnetic flux through the coil change ?
However, I am thinking about this as being a dummy ,meaningless, assumption to make the evaluation of the solution to the RL circuit differential equation easy! So, why is the current equal to zero!

The back emf is related to the rate of change of current.

$$V = -LI'$$

or

$$V = -L\frac{dI}{dt}$$

When a voltage is "applied" to an inductor, then (ignoring things like the resistance of the wire and stray capacitance) the back emf will be equal to the applied voltage.

When the applied voltage is 0, then (ideally at least) the current doesn't change with time.

If the applied voltage changes to say 10V, and the inductance is 1mH, then the current will change at a rate of 10/(0.001) = 10A / mSec. [Of course, as the current increases, it is likely that the voltage drop across the inductor will decrease. This will happen, for example if there is a resistor in series with the inductor.]

Now, when your teacher said that at t=0 the current is 0, it is probably because before that time, the current was 0. Typically, in examples like this, there is a switch that is open before t=0, and closes at t=0. It is the fact that the current was initially 0, that it is still 0 at t=0. Just as, if a car is initially at rest, and starts accelerating at t=0, then its velocity at t=0 will be 0.

• This was how I was looking at it.Thanks! May 6, 2021 at 15:45

It might help to visualize this as follows:

It is impossible to instantaneously assign a current through an inductor, for the same reason it is impossible to instantaneously assign a velocity to a mass. In either case, an infinite effort variable (voltage or force) would be necessary.

You can instead instantaneously apply a voltage across an inductor, for the same reason you can instantaneously apply a force to a mass. In either case, the resulting flow variable (current or velocity) starts from zero and builds up to its steady-state value.

• So, based on your own argument if we applied a voltage through a resistance, the current can not go instantaneously to a steady-state value which is determined by Ohm's law, which I think is not true, the current does reach a steady-state value instantaneously. May 6, 2021 at 15:49
• @saidsalah2020, no, that is not true; a pure resistance can have any arbitrary voltage or current (but not both simultaneously) imposed instantaneously on it, to which it instantaneously responds with a current (in the case of an imposed voltage) or a voltage (in the case of an imposed current). This is not true for an inductor, whose impedance is set by the rate of change of the current: an infinite (discontinuous) change in current produces an infinite resistance to current flow. May 6, 2021 at 15:56