Why Is the Time Constant in an LR Circuit L/R Instead of L×R?

[Genji Shimada]

Homework Statement

Hi. I started studying LR circuits and the first thing that made me do searches in textbooks of mine and in the internet was the time constant which is surprisingly not L times R, but L/R which would mean the time needed to store and release energy is being prolonged with decreasing the R. I am trying to visualize this in the same manner as i visualize RC time constant ( Resistance increases which decreases the rate at which charge flows and it takes more time for the charge to eventualy build up on the plates). Yet i can't get a simillar logic with LR circuit. I have one explanation of my own bellow, but i doubt a bit that it's right.

Homework Equations

The Attempt at a Solution

This is the way i think about it:
When you initially close the switch, the current through the inductor would try to rise from 0 to its maximum value, but this changing I would create an expanding magnetic field which would induce counter emf. And so because of that, the current won't immediately reach its maximum value. Instead, every 1time constant this current will rise by 63,2% of the final minus the previous value. When it reaches maximum there is no more expanding magnetic field and the emf disappears. During this time the inductor is "charging". By increasing the resistance, we decrease the value of the maximum current and so the current through the inductor would reach its maximum earlier. This alone would mean that if R increases the time constant decreases. For discharging > since the current through the inductor is now smaller since we increased the resistance, the magnetic field created by it is weaker. And when we turn off the power supply, there will be less emf induced and thereby this emf will disappear quicker.

 

[scottdave]

That is one way to think about it.

 

[gneill]

By increasing the resistance, we decrease the value of the maximum current and so the current through the inductor would reach its maximum earlier.

That's not true if you consider your "63.2%" argument. Once the circuit is set, the time constant is fixed and the maximum current is fixed.

Suppose you doubled the voltage supply potential without altering any other component values. The maximum current would double, but would the time constant change too?

 

[scottdave]

That's not true if you consider your "63.2%" argument. Once the circuit is set, the time constant is fixed and the maximum current is fixed.

Suppose you doubled the voltage supply potential without altering any other component values. The maximum current would double, but would the time constant change too?

Good point. I had to re read the original post, I missed that at first.

 

[Genji Shimada]

I shall think more on it and post later, thanks!