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Current phenomena in Inductor

09/13/2008 11:39 AM

Hai friends Could anybody clarify me "why the current flowing in Inductor lags behind the supply Voltage"?????????? Kindly clarify me in terms of analogous form & in terms of Theoretical manner in terms of Derivation.......Please............

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Murali Shankar S.L
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#1

Re: Current phenomena in Inductor

09/13/2008 12:32 PM

hey brother,

consider a DC battery connected to a coil of wire. electric flow starts through the coil and creates a magnetic field as it does . the magnetic field appears to oppose the current flow through the inductor as current is increasing, because the magnetic field is "sucking " energy out of the coil. the magnetic field dampens or opposes changes in current flow, the magnetic field collapses back into the coil if current flow decreases,

voltage leads current through an inductor. current leads voltage through a capacitor.

"ELI the ICE man". hope this helps. Dan

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#2

Re: Current phenomena in Inductor

09/13/2008 12:45 PM

Hey Mshankar.85,

I can point you in the general direction.

Current flowing in a conductor produces a magnetic field, but there must first be a potential for current to flow, by definition. In an inductor, the conductors are necessarily in sufficiently close proximity for the field of one loop to be inside the field of the adjacent loops. Any charge flowing through that field will be affected by it. Since the electrons flowing around the surface of a conductor are largely responsible for transmitting the current, and since electrons are negatively charged, they will necessarily be affected (held back somewhat) by that field as they race around to feed the load. So you have to look for a field charge calculation, which I think I remembered from back in either electronics or physics coursework. (but that was over 20 years ago, so memory is foggy there, sorry)

Now as I understand it, by definition a conductor will also conduct through the material, so as soon as the switch energizes the windings, the whole conductor is immediately "at the voltage potential of the circuit". Hence, E (voltage) Leads I (current) in an L (inductive ciruit, i.e. motor or coil). This implies to me that you have to find some equation relating the surface area & resistance (per unit length L, perhaps?) of the conductor to the field effect above.

This is the best I can do, good luck.

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#3

Re: Current phenomena in Inductor

09/13/2008 1:05 PM

As you know, the electromotive force around a loop, b, due to current in another loop, a, is given by

bE•dl = -dφab/dt = -Mab dIa/dt

where the integral is actually a closed path (I don't have that symbol handy). So, in an inductor coil, a and b are simply adjacent turns.

So, if the current is sinusoidal, you know the derivative of a sine to be a cosine, which is 90° out of phase. It is more informative to say that the voltage leads the current.

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#4

Re: Current phenomena in Inductor

09/13/2008 11:04 PM

The definition of inductance is in the equation:

V = L di/dt

The potential drop across the inductor is proportional to the current rate of change. Saying that the voltage leads the current, is a special case of the general statement in the frequency domain. If you don't understand that, plot a sine wave and its first derivative, the cosine.

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#5

Re: Current phenomena in Inductor

09/14/2008 9:12 AM

say you apply a voltage of Vm*Sinωt to terminals of a coil that has an inductance of L.

Acc to the Faraday law: VL= L*di/dt or inversely; iL= (1/L)VL.dt

means iL= (1/L)∫Vm*Sinωt.dt = -(1/L)*Vm*Cosωt

Since -(Vm/L)*Cosωt = (Vm/L)*Sin(ωt - ∏/2) then:

voltage v(t) ≡ Sinωt

current i(t) ≡ Sin(ωt +φ) = Sin(ωt - ∏/2).

This is why we say that the current lags voltage by ∏/2 (90o). If it were +∏/2 the phase difference (φ) then we would say current leads voltage by 90o.

In fact the phase difference (φ) can never reach to the value of ∏/2 'couse of the resistances and capacitances in the circuit.

i hope this help.

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#6

Re: Current phenomena in Inductor

09/15/2008 2:16 PM

From the analogous perspective: ---- (and don't take this too seriously, just accept it)

In a mechanical system;

Capacitance is like stored energy (air pressure) in a pneumatic cylinder or water pressure in a hose. The charge (voltage - electrical energy) between the plates of a capacitor is ready to flow at the slightest provocation, thereby producing a current.

Inductance is like a metal spring under tension or compression. However the energy (from current flow, not voltage) in an inductor is stored as a magnetic field. The conversion from electrical energy to magnetic and back requires current flow which is like my mother-in-law - always late because she is always pushing back.

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