Electromagnetic vibrations, like mechanical ones, are of two types: free and forced.
Free electromagnetic oscillations, always damped oscillations. Therefore, in practice they are almost never used. While forced vibrations are used everywhere and everywhere. Every day you and I can observe these fluctuations.
Alternating electric current
All our apartments are lit using alternating current. Alternating current is nothing more than forced electromagnetic oscillations. The current and voltage will change over time according to the harmonic law. Fluctuations, for example, in voltage can be detected by applying voltage from an outlet to an oscilloscope.
A sine wave will appear on the oscilloscope screen. The frequency of alternating current can be calculated. It will be equal to the frequency of electromagnetic oscillations. The standard frequency for industrial alternating current is assumed to be 50 Hz. That is, in 1 second the direction of the current in the socket changes 50 times. US industrial networks use a frequency of 60 Hz.
A change in voltage at the ends of the circuit will cause a change in the current strength in the oscillatory circuit circuit. It should still be understood that the change electric field does not happen instantly throughout the entire chain.
But since this time is significantly less than the period of voltage oscillation at the ends of the circuit, it is usually believed that the electric field in the circuit immediately changes as the voltage at the ends of the circuit changes.
The alternating voltage in the outlet is created by generators in power plants. The simplest generator can be considered a wire frame that rotates in a uniform magnetic field.
The magnetic flux penetrating the circuit will constantly change and will be proportional to the cosine of the angle between the magnetic induction vector and the normal to the frame. If the frame rotates uniformly, the angle will be proportional to time.
Consequently, the magnetic flux will change according to the harmonic law:
Ф = B*S*cos(ω*t)
The rate of change of magnetic flux, taken with the opposite sign, according to the EMR law, will be equal to the induced emf.
Ei = -Ф’ = Em*sin(ω*t).
If an oscillatory circuit is connected to the frame, the angular speed of rotation of the frame will determine the frequency of voltage oscillations in different sections of the circuit and the current strength. In what follows, we will consider only forced electromagnetic oscillations.
They are described by the following formulas:
u = Um*sin(ω*t),
u = Um*cos(ω*t)
Here Um is the amplitude of voltage fluctuations. Voltage and current change with the same frequency ω. But voltage fluctuations will not always coincide with current fluctuations, so it is better to use a more general formula:
I = Im*sin(ω*t +φ), where Im is the amplitude of current fluctuations, and φ is the phase shift between current and voltage fluctuations.
Alternating current- this is in a broad sense electricity, changing over time. Most often, this change occurs according to a sinusoidal law I = I 0 sin( ω t+φ). This is exactly the current that industrial current sources generate.
In different sections of a linear conductor, the current strength is the same, but over time it changes according to a periodic law. Each current value is repeated after a period of time T=2π/ ω, which is called period-house, and the magnitude ω — angular frequency. Frequency stability is an important quality of alternating current. The argument of sine is the quantity ω t + φ - called phase(it's useful to abstract from geometric meaning sine and do not perceive the argument of sine as a certain angle).
With constant current, electrons move in a thin conductor like water in a pipe, but at alternating current each of them performs oscillatory motion along the conductor as harmonic oscillator. The amplitude of these oscillations is very small, and within a single conductor all electrons oscillate in phase, that is, synchronously. If to a source with voltage U a circuit including a capacitor is connected, then (consequence Ohm's law)
U =IR + (q/C) —ε.
Here the first term on the right side is the voltage drop across the resistance, the second - across the capacitor ( q- capacitor charge), third - EMF outside forces operating in the area under consideration. Power, allocated in this chain is determined by the equality
N=UI
This Job, which the source performs per unit time.
If U- AC voltage, U =U 0 sin ω t, A ε — Self-induced emf, ε = - L(ΔI/Δt), alternating current flows through the circuit: I =I 0- sin (ω t + φ), and
I 0 = U 0 /√ (R 2 + (Lω — 1 / ω C) 2),
tgφ = (1 / ω C—ω L)/R.
If there is no capacitor, you should put 1 / C=0. From the formula, taking into account the formula, we find:
N = UI = U 0 sin ω t × I 0 sin (ω t+φ ) = U 0 I 0 ( sin 2 ω t× cos φ + sin ω t cos ω t sin φ ).
This is the power value at time t. The average power value over the period is equal to:
(The average value of the square of the sine over the period is ½, and the product of the sine and cosine is zero.) Quantities U eff =U 0 /√2, I eff = I 0 /√2 are called effective values AC voltage and current. It is these quantities that are meant when talking about the strength and voltage of alternating current. Material from the site
Let there be a box with an unknown filling. On pointA a conductor with current strength I enters the box, at a pointBa conductor comes out with the same current strength. Voltmeter shows voltageU effbetween pointsAAndB.The formula determines the power released in the box. If this power is positive (cosφ > 0), then either heat is released in the box, or an electric motor is hidden, doing the corresponding work, or both. Ifcosφ < 0, то в ящике скрыт генератор тока. Ес-ли мощность близка к ну-лю, а ток не equal to zero, in the box there is a capacitor or coil with high inductance. (The power released is positive if at a given moment the current flows towards the lower potential.)
When there is no load, the current in the primary winding transformer is determined by the formulas, taking into account the fact that 1 /C = 0, and power consumption - by the formula. Phase differenceφ close to -π/2, and power consumption is low. When a load is connected, a current appears in the secondary winding, which induces an additional current in the primary. The phase difference changes and the power consumption increases.
On this page there is material on the following topics:
The left diagram below shows the connection of two diodes in an alternating current circuit. In this case, the upper parts of the sine wave pass through the upper diode (in the direction of its “arrow”), and the lower parts of the sine wave do not pass through the lower diode (against its “arrow”). Thus it turns out pulsating unidirectional current, and exactly half of the original power does not reach the consumer, since “plains” with zero current are formed. For those especially interested in physics, we note that exactly the same result will be if you leave only one diode, any one at that.
The right diagram shows the inclusion of four diodes according to the so-called bridge circuit. It is more advantageous compared to the previous one: diodes pass in pairs both the upper and lower parts of the sine wave, respectively, to the “+” and “–” terminals. As a result, from the initial alternating current, on the graph of which one can conditionally distinguish “hills and ravines,” on the graph of the resulting unidirectional current, “not hills and plains,” but “double hills” are formed. This means that now all the power of the original current reaches the consumer.
And in conclusion, let's look at how the Joule-Lenz law can be applied to non-constant current Q=I²Rt, describing the thermal effect of current. What if the current strength is constantly changing? It is necessary to replace it with a conditionally constant current, which produces the same thermal effect. In physics, such a conditionally constant current value is called equivalent(effective, effective) value of the intermittent current strength.
Definition: equivalent value of intermittent current is equal to the value of such a direct current, which, passing through the same resistance, releases the same amount of heat in it in the same time. It is the equivalent current value that all ammeters show us. The same applies to voltage and voltmeters. So, it is possible to determine the equivalent values of non-constant currents calorimetric measurements(see § 06-c).
- Semiconductor diode is an electrical device...
- On the left halves of both diagrams there is...
- When a sinusoidal current is applied to the “input” of the circuit with two diodes in the left diagram, the following happens: ...
- Diodes separating the sinusoidal current circuit from the right side of the circuit ultimately result in...
- The pairwise transmission of both parts of the sinusoid is realized in...
- The use of exactly four diodes ultimately leads to the fact that...
- Can also be applied to alternating currents...
- To apply the Joule-Lenz law in the case of variable current strength, it is necessary...
- A conditionally constant current value leading to the same thermal effect is called...
- Let us remember: the equivalent value of a non-direct current is such a value...
- Experimentally compare the equivalent values of any two currents...