A doubt about inductors and capacitors

derek10

[/itex]Hi I am new here

I know (correct me if wrong please ) that inductors store current in its magnetic field, and capacitors store voltage in its electric field

But, why when disconnecting a inductor charged from a DC circuit, a spark is produced at the disconnected point and it loses its energy while the capacitor not and the electricity is stored like a battery? I understand that [itex]I = \frac{V}{R}[/itex] and the spark in inductors are produced because Voltage rises to compensate the resistance when opening the circuit but, why does a capacitor voltage stay the same despite no current and infinite resistance and a inductor discharges immediately at the same circumstances?
Many thanks.

Simon Bridge

That would be a very confused way of putting it yes.

Capacitors store energy in their electric fields.
Inductors store energy in their magnetic fields.

Inductors cannot become "charged" in a DC circuit ... in a steady-state DC circuit they look like a short circuit and act as an electromagnet. If you disconnect one, the collapsing magnetic field induces further current in the coil.

Where inductors are just a wire (short circuit) in DC, capacitors are a gap (open circuit). The power supply just moves charge from one side of the gap to the other. Disconnect the supply and there is no path for the charges to get back ... so the charges get stored.

In the fluid-analogy for electric circuits, a capacitor is a water-tank. I don't think there is an equivalent to an inductor.

AlephZero

If a flow or water corresponds to the current, a sort of analogy would be a propellor in the water pipe that all the water has to flow through, turning a heavy wheel. When you apply some water pressure, the flow/current can only increase slowly because it takes time to get the wheel spinning. If the flow is steady, the wheel doesn't affect it (ignoring friction, which corresponds to the resistance of the wire in a real inductor).

If you try to stop the water flow suddenly, you get a huge pressure (voltage) because the kinetic energy in the wheel is still trying to pump the water through the propellor, but the water has nowhere to go - except possiblly to burst the pipe (send a spark across the electrical switch).

OK, that's not so good as some of Maxwell's mechanical analogies for EM fields built from infinte arrays of gyroscopes coupled together with linkages - but it's a start.

It could be fun making a real device like this plus a water tank to simulate an LC circuit - a project for a science fair, maybe? Demonstrate resonance by rasiing and lowering the tank a bit, and sloshing water everywhere if you do it at the right frequency....

Simon Bridge

That's not bad: water-wheels are usually used to represent light-bulbs. But you are right - when the flow stops the wheel wants to keep going.

truesearch

A collapsing magnetic field induces an emf. There can only be an induced current if there is a complete circuit.

Simon Bridge

Well OK - though you can have a current without a complete circuit, the cited example did involve a spark so presumably the emf was strong enough to push charges across the gap.

mfb

The analogy of a disconnected inductor (static case: no current flow) is a short-circuit for a capacitor (static case: no voltage).
And a disconnected capacitor (infinite resistance) corresponds to a inductor with a short-circuit (no resistance).

truesearch

Faradays laws state how to calculate induced emf not induced current.

rbj

not the best fluid analogy for a capacitor. a better analogy is a cylinder with a spring-loaded piston inside.

sure there is. a water turbine with the turbine shaft connected to a flywheel.

256bits

Yes dualogs and analogs - I think you mean dualog. Analogs rather refers to system elements of the same type.

Wikipedia must have a good long discussion for any reader wishing to expand their knowledge.

256bits

We usually think of a DC circuit being connected to a voltage source. A capacitor will charge up only to the value of the voltage of the battery and then no more current will flow. For an inductor connected to a battery the rate of change in current is what gives the 'resistance' to the battery, so if you have a strong enough battery and your inductor is constructed well enough, then very high currents can be achieved.

But, if you consider a current source, then since the current is not changing then no voltage will be observed across the inductor. On the other hand, the current source is continiously pumping current into a capacitor which can then charge up to very high potential. You can then witness sparks across a gap when the voltage becomes high enough. I am not absolutely sure but storm clouds would acquire the high potentials this way and you would call the discharge lightning and thunder.

cabraham

I don't wish to be rude, but that is only partially correct. Faraday's Law, herein "FL", relates magnetic flux to voltage. Specifically, FL relates net flux to net voltage. When a time-varying magnetic flux is present in the vicinity of a conductor, a Lorentz force acts on the conductor's free electrons, resulting in charge motion, which is current. If the path is open, current does indeed flow, but it is called a displacement current, which can be small, or at very high frequencies, quite large.

If the loop is open, charges accumulate at each end, and there is an emf across the gap between the 2 ends of the conductor. As the mag flux varies with time, these charges move and displacement current continues. Even with an open path there is current as well as voltage.

If the loop is closed with a resistance R, obviously we have conduction current as well as displacement current. Assuming it is low enough frequency where conduction is much greater than displacement. The current in the loop has its own magnetic flux encircling the conductor. Per law of Lenz, LL herein, its polarity is opposite to that of the external field. So the actual flux enclosed by the loop is the sum total of the external plus the internal flux associated with the current in the wire.

We have mutual & self induction going on simultaneously. FL states that the voltage one time around the loop equals the negative of (LL) the time derivative of magnetic flux. But we must remember that the voltage, or emf if you prefer, is a net quantity, as is the flux.

A good example is to let the loop be superconducting. The voltage once around the loop becomes zero. This is due to the current in the loop having a magnetic flux around the wire that cancels the incoming external flux. Hence we have zero emf.

If the loop resistance R, is not zero, but very small, we have about the same current, and a very small voltage. Again, per LL, cancellation takes place. But if the loop R is made larger than a critical value so that the loop current is too weak to produce a magnetic flux that cancels the external flux, then the flux "phi" in FL, is essentially the external flux. Increasing R results in a loop emf that hardly changes. When R is large, the internal flux generated by the loop current is very small compared to the external incoming flux, and the net flux is very nearly that of the external flux. Under these conditions, we can state that the induced voltage, i.e. work per unit charge once around the loop, is the negative of the time derivative of the external flux.

But for low values of R, we cannot make that assumption. I don't wish to nitpick, but that is a point that should be made. I will elaborate if needed. Best regards.

Claude

truesearch

I have a limited range of about 12 A level text books and none of the explanations therein relate to anything posted here. I know that an emf involves charges separated and that means there must have been a 'current' for however long.
I will confine my interest to the text book explanation of faradays law in terms of induced emf and rate of change of flux linkage.
I am vaguely interested in how you would calculate the currents you allude to (or the voltages) but it looks like it will be beyond me.
The original post is from someone new here and I hope that he is able to pick his way through everything posted and come out wiser.

cabraham

http://www.physicsforums.com/showthr...46#post2163546

The above link is to a computation sheet I posted a few years ago. A loop which has a resistance R, inductance L, frequency omega, & external flux phi_e, can be computed for current, voltage, & internal flux phi_i. I will elaborate if needed.

Claude

truesearch

I read your computation sheet which is interesting. Is it published in any recognised text books?
I cannot find a recognised text book that states anything other than
Induced emf = rate of change of flux linkage. none state any reference to induced current as a version of faradays law. There must be a good reason for that !
It is misleading to confuse the 'displacement' current, ie the movement of electrons giving rise to the induced emf with the induced current in a complete circuit resulting from said induced emf.
anyone wanting to get to grips with faradays law should stick to the text book explanations.

cabraham

It depends on the text you are reading, as most refer to devices powered from a CVS (constant voltage source). Transformers, motors, & generators are often explained using FL. A xfmr is a good starting point. A CVS energizes the primary & flux is established in the core. The flux relation with input emf is given by FL. An important condition is that the primary flux couples the secondary winding almost at 100%, & vice-versa.

The secondary voltage is also given by FL, & from FL we get that Vs/Ns = Vp/Np. The secondary & primary voltages scale according to the turns ratio. If a load is connected to the secondary, current will flow. A magnetic flux will be present which tends to cancel the core flux due to the primary emf source. The secondary voltage will tend to drop. As you draw more secondary current, the secondary voltage goes down. But before that can happen, something else takes place.

When the secondary is open, the core flux induces a counter-emf, cemf herein. This cemf opposes the source emf. The exciting current in the primary is the difference between the CVS value & the cemf, divided by the primary impedance. This exciting current consists of loss current plus magnetizing current in quadrature. The magnetizing current times the primary turns is the mmf.

When secondary current is drawn due to loading, the magnetic flux of the secondary current induces a counter-counter-emf, or ccemf herein. The ccemf opposes the cemf which opposes the source emf. The secondary current times secondary turns is the counter-mmf or cmmf. The primary current is now as follows. The ccemf adds with the source emf, and the cemf subtracts. Hence the primary current goes up so that its amp-turns balance the loaded secondary amp-turns.

But the primary amp-turns produces counter-counter-mmf, ccmmf, & counter-counter-counter-emf, cccemf. The result is that the secondary voltage drops only a small amount, owing to resistance & leakage reactance in the windings. Hence the secondary voltage is very close to what FL predicts w/o the need to bother with internal/external flux components cancelling.

The cancellation of fluxes is mitigated by the primary current increasing so that constant secondary voltage is maintained. That is why you can simply compute the secondary voltage per FL even though loading currents are present.

But now, let us change conditions. A magnetic flux is radiated from a radio station antenna. A loop located miles away encloses this flux & induction takes place. The coupling from the loop back to the broadcast tower antenna is nowhere near 100%, typically a fraction of 1%. So now if a loop encloses a flux, & the loop is open, or has a very high R value closed, the inducred voltage can be computed per FL, w/o the need to consider internal flux & cancellation.

But if the R is low enough, the loop current magnetic flux cancels the external flux & the voltage drops. Because of loose coupling to the radio station source antenna, the current in the antenna DOES NOT INCREASE as a result. The counter-counter-emf in the loop due to load current does not get mitigated by increased current back at the source.

That is my point. As a check, take my equations, & use the condition that R is much greater than omega*L. The quantity omega*L is the inductive reactance X_L. Let R >> X_L. Notice that the voltage induced is independent of load & exactly as stated per FL. I'll leave that as an exercise for anyone interested. Also, I, the loop current, is simply V/R.

But should R fall in value, or X_L increase in value due to increased frequency, then we must use the full expression, the more complicated computation. Again, I will elaborate if needed.

Claude

truesearch

I don't wish to be rude but an analysis of transformer action and radio wave propagation does not clear up any misunderstandings about Faraday's law.
My reading of text books is that a changing magnetic flux linkage produces an emf in a conductor. There is no 'induced current' unless there is a complete circuit (I accept that a 'spark' does constitute a complete circuit of sorts).
There are countless published questions at A level (that is what I teach) along the lines of : A plane coil of 10 turns and area 0.1m^2 is placed with its plane at right angles to a magnetic flux of 2T. The flux decreases uniformely to zero in 0.8s, calculate
a) the emf induced across the ends of the coil
b) the current induced in this coil.
I wonder how you would respond to a question of this sort and what use you would make of the laws of electromagnetic induction.
I bet a pound to a penny you would get the same answer as me and there would be no mention of 'displacement' current