# why there is phase difference of 90, in Inductor load?

Discussion in 'General Electronics Chat' started by amit_telar, Jan 7, 2009.

1. ### amit_telar Thread Starter New Member

Jan 3, 2009
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Dear All

why there is phase differance of 90, in Inductor load? why it has not zero phase shift as Resistor has?

Thanks & Regards
Amit

Apr 20, 2004
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3. ### mik3 Senior Member

Feb 4, 2008
4,846
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If the inductor is ideal the equation relating the current through and the voltage across it is:

v=L*dI/dt

If I=A*sin(ωt)

v=L*A*ω*cos(ωt)

sin and cos have a 90 degrees phase shift, that's why voltage leads current by 90 degrees.

4. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,047
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Hi, Mik:

While this is all absolutely true, I don't think it gives any physical insight as to why an inductor does what it does. I think our poster is looking for somethinig tangible to grasp.

I like to think of an inductor as a big spring....like a slinky with a weight hanging on one end. If you suddenly lift the top end of the slinky a couple of inches, it takes a while for the weight to fiinally respond, and rise accordingly. It's not a perfect analogy, but it's sufficiently physical to have some meaning.

Just a thought

eric

5. ### StephenDJ Active Member

May 31, 2008
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I'd think I'd like to put this in some practical terms. Let's face it - the current though an inductor cannot change unless the magnetic field that surrounds it has time to catch up to speed. It takes TIME for the field to "charge up" and begin agreeing with the desired level of the flow of current. This is where your delay come from.

6. ### steveb Senior Member

Jul 3, 2008
2,433
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This is incorrect. The correct explaination was already given by mik3.

Note that magnetic flux is inductance times current with no delay.

i.e. $\lambda = L \; I$

Take the derivative of both sides assuming constant inductance.

${{d\lambda} \over {dt}} = L \; {{dI} \over { dt}}$

Note that rate of change of flux is voltage, hence

$V= L \; {{dI} \over { dt}}$

Note that a perfect inductor has no delay between current and magnetic field. The phase difference is between voltage and current as explained by mik3.

EDIT: Additional comment - there are cases where flux lags current, but not in the case of a perfect inductor. Restistance in a coil, or lossy cores cause delay, but this is a separate effect.

Last edited: Jan 8, 2009
7. ### mik3 Senior Member

Feb 4, 2008
4,846
63
Lets see it in another way. If current tried to increase in an inductor as changing magnetic field is created which induces an EMF across the inductor (self inductance). This EMF has a polarity which opposes the applied voltage and thus the current is increasing slower than the applied voltage is.

8. ### StephenDJ Active Member

May 31, 2008
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I fully agree, mik3. The EMF has a polarity which opposes the applied voltage! But why does the current increase more slowly? Isn't there a voltage drop across the inductor at this instant? And if so where the force from the applied voltage being absorbed? It's keeping the current from instantly flowing, so where is all this energy from the applied voltage going, or being absorbed? Into the field??

9. ### mik3 Senior Member

Feb 4, 2008
4,846
63
You want to get deep into that but I am not a physic.

The energy from the supply voltage goes into the magnetic field. The field is not created from nothing!

10. ### StephenDJ Active Member

May 31, 2008
58
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Oh okay, so that's where the voltage drop comes from (the field soaking up the energy). I'm sorry I have to get so technical. (smile) I love it! But that's why I'm here.

Last edited: Jan 9, 2009
11. ### steveb Senior Member

Jul 3, 2008
2,433
469
It is very difficult to really explain things like this. I think we just become comfortable with concepts through familiarity. Then we mistake this for understanding.

Mechanical concepts seem to be easier to accept intuitively because we see and feel mechanical systems much easier than electrical systems.

Here we can make an analogy with mechanics. Replace inductance L with mass M; voltgae V with force F and current I with velocity U. Now compare.

F=M* dU/dt

V=L*dI/dt

The inductance L is like the inertia M in Newtons force law. When voltage is applied to a coil, the current does not immediately flow. This is the same as putting a force on a mass. The mass does not immediately develop velocity when force is applied.

Does anyone really understand why F=ma is true? Well, yes it results from conservation of momentum, but why is momentum conserved? Well, we just know it's true by experimentation.

Similarly, V=L*dI/dt results from Maxwell's electromagnetic equations which we know are true through experiments.