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Originally Posted by DerAlte Thamba! Here current is not static as in DC circuits, it is dynamic - no movement of VC, no current. So both EMF and current are time-dependent. That is why the differential equation.
Simplified, d(EMF)/dt = dI/dt*(coil impedance). Current is produced by the coil moving in the mag field, which produces and EMF across the L and R of the coil. |
Well, I was trying to avoid differential equations as promised. I assumed "v" to be constant in the "illustration". That doesn't mean VC is not moving. If it is stationary, then anyway v=0! For understanding purpose, you can think of it as a "point" in time where a particular value of v is applicable, and the coil obviously moves only by distance "delta-x" which is by definition described as "infinitesimally close to, but not equal to zero"
. An other option is to assume that the coil is really moving with a constant v, which also means that you have to assume that the driver has unlimited Xmax! (next version of XBL^2 => XBL^infinity)
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- the damping is by ENERGY DISSIPATION (taking away energy from the moving SYSTEM), not mechanical opposition. Shorted coil takes away mechanical energy and dissipates it as heat energy by way of the electrics.
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Yes, "energy dissipation" is the standard definition of damping. But if you analyze it carefully, dissipated energy and the opposing force are closely related, they are just two sides of the coin.
OK, what is dissipation?.... Energy can neither be created nor destroyed, so dissipation= conversion into heat. But then how would you define dissipation if you were talking about a system whose purpose is to produce heat (say a geyser)? I guess if it creates some sound pollution, then that should be called it's dissipation...exactly opposite, you see!
So what is getting "dissipated"?...coil's motion is getting dissipated as heat. We don't want it to move by itself, i.e. it should stop as quickly as possible once the amp's signal becomes zero or when amp is feeding some signal, it should strictly follow the command without deviating. Basically the opposite force that I was talking about actually stops its motion by indirectly converting it into heat. The point is that the work done by that opposite force must be the same as heat dissipated (and you should be able to believe this even without looking into equations, right?). That is nothing but what we are calling damping. How good the coil is at that depends upon how fast it can do it.
Let us tally, by calculating how fast the heat is dissipated (i.e. power) instead of the mechanical force. Please stick to the assumption that I made, it should be enough for understanding purpose, and my previous simple equations can be reused.
Power dissipated in one single turn or a ring:
= I^2 * R
= (K1/R)^2 * R
= K1^2 / R
= K1' /R (K1' => another constant)
Power dissipated in N separate rings:
= K1' * N/R
Power in case of whole coil with N turns:
= (K1/R)^2 * NR
= K1' * N/R
The bottom line is that it is proportional to N/R in both cases with same constant of proportionality. They are providing same power dissipation, so same amount of damping.
We can even tally with the mechanical power also, you have to just multiply Ftotal by v. So if v is same, mechanical power in both cases is also same. In fact if one resolves K2, it should be
exactly equal to the electrical power dissipation
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More turns, more R, more Pdiss (R*I^2). Bell curve:
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Does my rambling make any sense, OEO?
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No..no... this is completely wrong. Before drawing any conclusion about how R affects the equation, you must be sure that I is independent of it, when rest of the system doesn't change. But in this case, I is dependent on R, EMF is not. So, you should use the equation EMF^2 / R instead of above. You are saying open circuit will dissipate maximum heat whereas a short will not dissipate anything at all? That would have been true for a given current, but it is exactly opposite for
a give voltae!!