What is a steady stream
Forum: Analog electronics and circuit technology Continuity current inductance justification
Hello, I have a basic question. The voltage across the capacitor is known to be constant. The current through the inductance is also constant. For example, I write for the voltage at the inductance L: u (t) = L di (t) / dt i (t) = 1 / L integral u (t) I have now heard a reason at university that I no longer have get together. It had something to do with the fact that the current has to be constant, otherwise you would get infinitely high energies ... Can anyone give me the reason again, possibly also based on: "If i were suddenly zero, then ..." Many Thanks
: Postponed by Admin
Coil: if the current were suddenly interrupted (or changed suddenly), then the voltage would rise or fall to infinity. (also try them, see ignition and switching sparks). Capacitor: replace current change with voltage change. Greetings, Peter
for the uni: If i were suddenly zero, then di / dt would become infinitely large for an infinitely short time and with it the voltage that drops across the inductance (1st formula). But it doesn't happen in reality. Before that there is lightning. Instead the freewheeling diode. Very few things in nature are discontinuous. Even a shock wave has - observed quickly enough - a slow rise. Here, for example: capacitive effects in the line, or the like. Energies are very rarely infinite (exception: the speed of light). Even with discontinuities. To do this, the energy of something would have to be the derivative. I do not know any such formula. Perhaps viewed differently: the energy in the coil is 0.5 L I * I if you manage to switch off the current completely, the energy jumps from E to 0 (discontinuity). This makes the power (dE / dt) infinite. Maybe that's what the prof meant.
If the current were discontinuous, its derivative dI (t) / dt would be infinitely large and thus, according to your first equation, U (t) as well. Even if it were possible to generate voltages as high as desired, the current through the coil would not jump, but the one around the coil (sparks, leakage current in the insulation material). > It had something to do with the fact that the current has to be constant, since> otherwise one would get infinitely high energies ... Theoretically, the energy would remain finite even if the coil current was discontinuous. Only the power would become infinite, but for an infinitesimally short period of time.
Timo Pat wrote:> Hello,> I have a basic question. The voltage across the capacitor is> as is well known, continuous. The current through the inductance is also constant. >> For example, I write for the voltage at the inductance L: >> u (t) = L di (t) / dt >> i (t) = 1 / L integral u (t ) >> I have now heard a reason at the university that I can no longer> get together. It had something to do with the fact that the current> has to be steady, otherwise you would get infinitely high energies ... >> Anyone who can give me the reason again, possibly also based on:> "If i were suddenly zero, then it would ... ">> Thank you very much Voltage on the capacitor Change in charge Q = C * U = I * t Change over to II = U * C / t If U is to jump by 1V, for example, then you need an average current I = 1V * C / t If t should go to zero, then I must go to infinity. I = 1V * C / 0s = infinite
In my opinion, there cannot be an infinitely large amount of energy. at least not on earth. a conversion of matter into energy is possible. consequently one "could" convert the entire earth into energy, that would give a huge bang, but the amount of energy released would not be infinite - just huge. In the case of coils, there is also the fact that the energy is stored in the magnetic field of the core (with the exception of air coils). when the core saturates, the energy storage is over and the current through the coil is only determined by the ohmic resistance of its winding. In this operating state, however, the coil no longer stores any energy, instead it burns all of the energy fed in. similar to an overflowing barrel.
Hello Timo, the underlying principle is that the field energy of the component can only change slowly and finitely. In the case of a capacitor, the field energy is 1/2 C U ^ 2. So with the capacitor the voltage is constant. For the coil, the field energy is 1/2 L I ^ 2. So the current in the coil is steady. You can go further with the idea and consider the following: a) the electrical or magnetic energy is contained in the electrical or magnetic field and b) the field spreads with the speed of light 1 / sqrt (epsilon µ) of the respective medium The emphasis is on the fact that the energy is contained in the field. So it is not the case that the energy remains in the component and the field is some dirty effect of the component's energy. The experimental evidence came with the discovery of electromagnetic waves. So: the energy is in the field and the field is spreading at the speed of light. Since, according to Einstein's theory of relativity, field energy can only move slowly and slowly, it takes a certain amount of time before it comes out of the field and back into the circuit. In my opinion, this is the field theoretical background that justifies the finite performance of the component. Unfortunately, I have not yet conclusively brought this consideration to the end (that is, in terms of a suitable example). But actually it should open. > I have now heard a reason at university that I can no longer> get together. It had something to do with the fact that the current must> be steady, otherwise you would get infinitely high energies ... Otherwise you would get infinitely great achievements, not infinitely great energies. Greetings, Michael
Quote yalu: Theoretically, the energy would remain finite even with a discontinuity in the coil current. Only the power would become infinite, but for an infinitesimally short period of time. @Timo Pat: This is also a very good explanation of how to make P.M.P.O. can explain. In relation to a C: If the C could supply a current of 1000A for an infinitesimally short period of time, then you would have a 5000W amplifier (P.M.P.O.) on the USB with an output voltage of 5V. That is usually enough for an advertising guy ;-)
That follows directly from U = L x dI / dt. If I changes suddenly, U becomes huge. If I even changes discontinuously, the derivative is not defined at all. Kai Klaas
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