Electrical Engineering: Ch 7: Inductors (2 of 20) Why Does an Inductor Behave Like an Inductor?

welcome to a lecture online now let's answer the question why does an inductor behave like an inductor well what do we mean by behaving like an inductor we'll remember that an inductor opposes a change in current only the change in current you can have current gorn's an inductor as long as the DC current the inductor will do absolutely nothing only when that turn begins to change either increase or decrease the inductor begins to do something the question is why why does an inductor do that well let's try to figure that out here we have a single loop we have a wire going up around the circle and coming back down so we have a single loop of wire here and let's send a current through that wire the current will then go around the loop like this and then if you use your right hand rule if you take your thumb and put it in the direction of the current then your fingers will curl in the direction of the magnetic field around any current wire or I should say around any wire that carries a current let's say I have a single wire here that carries a current in this direction you could then take your thumb point in the direction of the current and your fingers will curl around the wire and the curl that fingers will show you the curl of the magnetic field the magnetic field will go around the wire like this so it's behind the wire and from the wire back behind the wire so the magnetic field that exists around a current carrying wire looks like this when that why it didn't gets put into a circle or a turn like this then you can see how the magnetic field will go through the loop inside this and not outside the loop on the outside so we have if you think about it the magnetic field comes back out of the loop around like this out of the board and then back into the board through the loop we're only concerned about the magnetic field through the loop we can say that there's what we call me kinetic flux through the loop in this case it's into the board because the direction the current like this and the amount of flux is simply equal to the strength of the magnetic field inside the loop times the cross-sectional area of the loop however big the loop is the bigger the loop of course the bigger the flux through the loop the mean filled inside a solenoid can be calculated to be the permeability of the in some types of free space or the core whatever the core is made out of times the number loops per unit length of the solenoid times the strength of the current notice that if you double the current you double the strength of magnetic field so the amount of flux the strength of magnetic field inside the loop simply depends upon the structure of the loop and the amount of current flowing through the loop now what happens when you increase the current well when you increase the current you will increase the minitek flux because in essence you've increased a magnetic field you increase the current which increases the magnetic field when you increase the magnetic field you increase the flux through the loop like you see here now what an inductor does an inductor opposes that change by setting up an EMF by inducing an EMF that causes a current to flow in the opposite direction which then causes the magnetic field in the opposite direction and so here I'm indicating with the little dots meaning that the magnetic field induced is coming out this way so this is the magnetic field that's induced by the coil by the loop which is caused by an EMF that's induced which caused a current to flow in the opposite directions now we have an induced current flowing in opposite direction which produces a magnetic field in the opposite direction which tries to stop the current from increasing in the first place and that's what an inductor does and during that small brief period in which it sets up an EMF as long as the current is changing an EMF is induced which sets up a current in the opposite direction with causes of magnetic field that tries to keep the original magnetic field from increasing so now we can say that the EMF that's induced here is like a voltage induced on the coil which is equal to the voltage across the inductor the V sub L remember the equation we showed you in the last video this was equal to the inductance times the rate of change the current with respect to time and the EMF induced according to what faraday found out so Faraday's laws now called EMF induced is equal to the number of loops in the term times the change of the flux through the loop per unit time so we can put that on the other side so for the magnitude of that then the number of loops times the rate of change of the flux through the loop with respect to time and of course the definition of the flux is at equal to the magnetic field times the cross-sectional area so here we can say that n times the D DT the rate of change of respect to time of the magnetic field times the area is equal to L times di DT now of course in this case we're going to leave the loop the same size so the area doesn't change but the strength of the B field does change and the B field can be found by replacing it by this quantity right there so this can now be written as n times a because the cross-sectional area doesn't change times the rate of change of the magnetic field in a magnetic field of solenoid is equal to this so it's equal to MU n I over L this and that is equal to L times di DT now all these things on the left side the equation notice that the permeability is a constant the length of the of the solenoid is a constant and the number of loops is a constant the only thing that changes is a current so this can now be written as n times n which is N squared times the permeability times the cross-sectional area divided by the length of the solenoid times the di DT the rate of change of the current respect to time is equal to the inductance times di DT and notice if you now compare the two equations notice we have the di DT on both sides but now we can see that the inductance of the solenoid is to this quantity right there the inductance L is equal to the number loops squared times the permeability of the core times the cross-sectional area divided by the length of the solenoid so there's another way in showing you why an inductor does what it does and from that we can see that the inductance of inductors simple depends upon the physical size the number of turns squared the permeability of the core the cross-sectional area and the length of the inductor and that's why an inductor does what it does it fights the change in the current

Channel: Michel van Biezen

Views: 31,762

Rating: 4.9703155 out of 5

Keywords: ilectureonline, ilectureonline.com, Mike, Mike van Biezen, van Biezen, ilecture, ilecture online, Electrical Engineering, Output, Input, Current, Voltage, Voltage Sources, Chapter 7, Ch 7, Inductors, Permeability, Oppose a change, Wires Wrapped Around a Tube, Resistors, Capacitor, Why Does an Inductor Behave Like an Inductor?, Magnetic Field, Magnetic Flux, Induced Current, EMF Induced

Id: sQmPABHR3b8

Length: 7min 1sec (421 seconds)

Published: Tue Jun 28 2016