Georg Simon Om began his research inspiring the famous labor of Jean Batista Fourier "Analytical theory of heat". In this work, Fourier represented a heat flux between two points as a temperature difference, and the change in the heat flux associated with its passage through the obstacle of the wrong form from the heat insulating material. Similarly, this ohm caused the occurrence of electric current by the difference in potentials.
Based on this, I began to experiment with different materials Explorer. In order to determine their conductivity, he connected them consistently and customized their length so that tok Power It was the same in all cases.
It is important at such measurements was to select the conductors of the same diameter. OM, measuring the conductivity of silver and gold, received results that, according to modern data, do not differ accuracy. So, the silver conductor in Ohm spent less electric current than golden. Ohm explained this by the fact that his conductor of silver was covered with oil and because of this, apparently, the experience did not give accurate results.
However, not only with this were problems among physicists, which at that time were engaged in similar experiments with electricity. Large difficulties with prey of clean materials without impurities for experiments, difficulty calibrating the conductor diameter distorted the test results. An even big snag was that the strength of the current was constantly changing during the tests, as variable chemical elements served as the current source. In such conditions, OM brought the logarithmic dependence of the current force from the resistance of the wire.
Few later German physicist Pogotendorf, specializing in electrochemistry, suggested that I replace the chemical elements on the thermocouple from bismuth and copper. OM began his experiments anew. This time he used a thermoelectric device running on the Seebek effect as a battery. It consistently connected 8 conductors from copper of the same diameter, but of different lengths. To measure the strength of the current ohm suspended with a metal thread over the conductor magnetic arrow. The current, walking parallel to this arrow, shifted her to the side. When this happened the physicist twisted the thread until the arrow returned to initial position. Based on the angle to which the thread was twisted, it was possible to judge the value of the current force.
As a result of the new experiment, OM came to the formula:
X \u003d A / B + L
Here X.- the intensity of the magnetic field of the wire, L. - Wire length, a. - constant voltage of the source, b. - constant resistance of the remaining elements of the chain.
If you appeal to modern terms for describing this formula, we will get that H. - current strength but - EMF source, b + L. - Total chain resistance.
Ohma law for a plot of chain
Ohma law for a separate section of the chain says: The current of the current on the section of the chain increases with increasing voltage and decreases with an increase in the resistance of this site.
I \u003d u / r
Based on this formula, we can decide that the resistance of the conductor depends on the difference in potentials. From the point of view of mathematics, it is correct, but false from the point of view of physics. This formula is applicable only to calculate the resistance on a separate section of the chain.
Thus, the formula for calculating the resistance of the conductor will take the form:
R \u003d P ⋅ L / S
Ohm law for full chain
The difference between the Ohm law for the full chain from the Ohm law for the circuit site is that now we must take into account two types of resistance. This is "R" the resistance of all components of the system and "R" internal resistance of the source of the electromotive force. The formula thus acquires the form:
I \u003d u / r + r
Ohma law for alternating current
The alternating current differs from constant by the fact that it changes with certain time periods. Specifically, it changes its meaning and direction. To apply Ohm's law here need to take into account that resistance in a constant current chain may differ from the resistance to the circuit with a current variable. And it differs if components with reactive resistance are applied in the circuit. Reactive resistance can be inductive (coils, transformers, chokes) and capacitive (condenser).
Let's try to figure out what is the real difference between reactive and active resistance in a circuit with alternating current. You have already needed to understand that the value of the voltage and current strength in such a chain changes over time and have, roughly speaking, waveform.
If we schematically imagine how these two meanings change over time, we will have a sinusoid. And voltage and current from zero rise to maximum valueThen, dropping, pass through the zero value and reaches the maximum negative value. After that, they rises again through zero to the maximum value and so on. When it says that the current or voltage is negative, here it is in mind that they move in the opposite direction.
The whole process occurs with a certain frequency. The point where the value of the voltage or current of the current from the minimum value climbing to the maximum value passes through zero is called a phase.
In fact, it is only a preface. Let's return to reactive and active resistance. The difference is that in the circuit with the active impedance of the current phase coincides with the voltage phase. That is, and the value of the current, and the voltage value reaches the maximum in one direction at the same time. In this case, our formula for calculating the voltage, resistance or current does not change.
If the circuit contains the reactive resistance, the current and voltage phases are shifted from each other to the ¼ period. This means that when the current reaches the maximum value, the voltage will be zero and vice versa. When inductive resistance is used, the voltage phase "overtakes" the current phase. When capacitance resistance is used, the current phase "overtakes" the voltage phase.
Formula for calculating the voltage drop on inductive resistance:
U \u003d i ⋅ Ωl
Where L. - inductance of reactive resistance, and ω - angular frequency (derivative in time from the oscillation phase).
Formula for calculating the voltage drop on capacitive resistance:
U \u003d i / ω ⋅ with
FROM - Capacity of reactive resistance.
These two formulas are special cases of the Ohm law for variable chains.
Full will look as follows:
I \u003d u / z
Here Z. - Full resistance of the variable chain known as impedance.
Scope of application
Ohm's law is not a basic law in physics, it is only a convenient dependence of some values \u200b\u200bfrom others that fits almost in any situations in practice. Therefore, it will be easier to list situations when the law may not work:
- If there is inertia charge carriers, for example, in some high-frequency electric fields;
- In superconductors;
- If the wire is heated to such an extent that the voltamper characteristic ceases to be linear. For example, in incandescent lamps;
- In vacuum and gas radiolams;
- In diodes and transistors.
Ohma law for alternating current in general, has the same appearance as for permanent. That is, with an increase in voltage in the circuit, the current also will increase in it. The difference is that in the AC circuit, the resistance is provided to it elements as an inductor inductance and a container. Given this fact, write the Ohma law for AC.
Formula 1 - Ohma law for alternating current
where Z is the total chain resistance.
Formula 2 - full chain resistance
In general, the impedance of the AC circuit will consist of active capacitive and inductive resistance. Simply put, the current in the AC circuit depends not only on the active ohmic resistance, but also on the size of the container and inductance.
Figure 1 - chain containing ohmic inductive and capacitive resistance
If, for example, in a DC circuit, turn on the condenser that current in the circuit will not be, since the constant current condenser is the discontinuity of the chain. If inductance will appear in the DC circuit, the current will not change. Strictly speaking, it will change, as the coil will have ohmic resistance. But the change will be insignificant.
If the condenser and the coil are included in the AC circuit, they will resist the current in proportion to the capacity and inductance, respectively. In addition, the phase shift is observed in the chain between voltage and current. In the general case, the current in the condenser is ahead of the voltage of 90 degrees. In inductance lags at 90 degrees.
Capacitive resistance depends on the size of the tank and the frequency of the AC. This dependence is inversely proportional, that is, with increasing frequency and capacity, the resistance will decrease.
After opening in 1831, the Faraday of electromagnetic induction, the first permanent generators appeared, and after and alternating. The advantage of the latter is that the alternating current is transmitted to the consumer with less loss.
With increasing voltage in the chain, the current will increase similarly by the case with a constant current. But in the AC circuit, the resistance turns out to be a coil of inductance and a capacitor. Based on this, write Ohma's law for AC: The current value in the AC circuit is directly proportional to the voltage in the chain and inversely proportional to the complete chain resistance.
- I [A] - the power of the current
- U [in] - voltage,
- Z [Ohm] - complete chain resistance.
Full chain resistance
In general, the impedance of the AC circuit (Fig. 1) consists of an active (R [OM]), inductive, and capacitive resistance. In other words, the current in the AC circuit depends not only on the active ohmic resistance, but also on the value of the tank (C [F]) and the inductance (L [GN]). The impedance of the AC circuit can be calculated by the formula:
Where 
The impedance of the AC circuit can be depicted graphically as a rectangular hypotenus, which has active and inductive resistance by custom.
Fig.1. Triangle resistance
Given the last equality, which will record the formula of the OMA law for AC:
- amplitude value of the current. 
Fig.2. Sequential electrical circuit of R, L, C elements.
From experience, it can be determined that in such a circuit of the fluctuation of current and voltage, they do not coincide in phase, and the phase difference between these values \u200b\u200bdepends on the inductance of the coil and the capacitance of the condenser.
They say: "You do not know the law of Oma - Sitie at home." So let's find out (remember), what is the law, and safely go for a walk.
The basic concepts of the law Ohm
How to understand the law Ohm? You just need to figure out what is in its definition. And to begin with the definition of current, voltage and resistance.
Current I.
Let the current flow flowing in some exhibitor. That is, the directional movement of charged particles occurs - let's say it is electrons. Each electron has an elementary electrical charge (E \u003d -1,60217662 × 10 -19 choulon). In this case, through some surface, a specific electrical charge will be held for a certain period of time, equal to the sum of all charged electrons charges.
The ratio of charge by time is called the current power. The larger charge passes through the conductor for a certain time, the greater the current power. The current is measured in Amperech.
Voltage U, or potential difference
This is just that thing that causes the electrons to move. Electric potential characterizes the ability of the field to make work on the transfer of charge from one point to another. So, between two points of the conductor there is a potential difference, and the electric field makes the charge of charge.
The physical value equal to the operation of an effective electric field when transferred electric chargeand called tension. Measured by B. Volta.. One Volt - This is a voltage that when charging the charge in 1 CL Makes a job equal to 1 Joule.
Resistance R.
The current is known to flow in the conductor. Let it be any wire. Moving along the wire under the action of the field, the electrons face the wire atoms, the conductor is heated, the atoms in the crystal lattice begin to fluctuate, creating electrons even more problems for movement. This is the phenomenon and is called resistance. It depends on the temperature, material, the cross section of the conductor and is measured in Omah.
Formulation and explanation of the Law of Ohm
The law of German teacher George Ohm is very simple. He says:
The strength of the current on the circuit site is directly proportional to the voltage and inversely proportional to the resistance.
Georg Ohm brought this law experimentally (empirically) in 1826 year. Naturally, the greater the resistance of the plot of the chain, the less the current will be. Accordingly, the greater the voltage, the and the current will be greater.
By the way! For our readers now there is a 10% discount on
This formulation of the Ohm law is the simplest and suitable for the chain section. Speaking the "section of the chain" we mean that this is a homogeneous area on which there are no sources of current with EMF. Speaking easier, this plot contains some resistance, but there is no battery that provides the current itself.
If we consider the law of Oma for the full chain, the formulation of it will be slightly different.
Let us have a chain, it has a current source, creating voltage, and some resistance.
The law is recorded as follows:
The explanation of the Ohm law for the hollow circuit is not fundamentally different from the explanation for the chain section. As we can see, the resistance is made up of the resistance and internal resistance of the current source, and instead of the voltage in the formula, the electromotive power of the source appears.
By the way, what is what EDC is, read in our separate article.
How to understand the law Ohm?
In order to intuitively understand the law Oma, we turn to the analogy of the current view in the form of a liquid. That was how Georg Ohm thought, when he spent experiments, thanks to which the law was opened, called him name.
Imagine that the current is not the movement of charge carrier particles in the conductor, but the movement of water flow in the pipe. At first, the water is raised by the pump to the waterproof, and from there, under the action of potential energy, it strives down and flows through the pipe. Moreover, the higher the pump runs water, the faster it flows in the pipe.
It follows the conclusion that the flow rate of water (current in the wire) will be the greater the greater the potential water energy (potential difference)
The strength of the current is directly proportional to the voltage.
Now let's turn to the resistance. Hydraulic resistance is the pipe resistance caused by its diameter and roughness of the walls. It is logical to assume that the larger the diameter less resistance pipes and those large quantity Water (larger current) will leak through its cross section.
The strength of the current is inversely proportional to the resistance.
Such an analogy can be carried out only for a fundamental understanding of the Ohm's Law, as its primordial appearance is actually a rather coarse approach, which, nevertheless, finds excellent use in practice.
In fact, the resistance of the substance is due to the oscillation of the atoms of the crystal lattice, and the current is the movement of free charge carriers. In metals, free carriers are electrons that have broken off atomic orbits.
In this article we tried to give a simple explanation of the Ohm's Law. Knowledge of these at first glance ordinary things can serve you a good service on the exam. Of course, we led it to the simplest wording of the Ohm law and will not climb into the debris of higher physics, dealing with the active and reactive resistance and other subtleties.
If you have such a need, our employees will be happy to help you. And finally, we suggest you to see the interesting video about the law Ohm. It is really informative!
Purpose: Experimentally determine the impedance of various loads and compare experimental values \u200b\u200bwith theoretical.
Theoretical part
Consider the relationship between the current and voltage in the AC circuit when the various loads are turned on (Fig. 29).
Ohmic resistance. Under this term understand the resistance of the conductor of the DC. In the future, we will consider quasi-stationary currents for which the instantaneous values \u200b\u200bof the current and voltage force denoted by small letters i. and u., obey Ohm and Joule-Lenza laws. The amplitude values \u200b\u200bof the current and voltage will be denoted I M. and U M..
Let an ohmic resistance applied voltage via the harmonic law:
U. = U M.cOS W. t., (31)
where W is the cyclic frequency of oscillations. According to Ohm's law through R. Current streams i.:
i. = I M.cOS W. t., (33)
From relations (32) and (33) follows:
1) the current and voltage phases on ohmic resistance coincide;
2) current and voltage amplitudes are associated with relation
Fig. 29. Ohomic, inductive and capacitive load
Inductive resistance. Let's give a coil with inductance L. and negligible low ohmic resistance, voltage changing by law (31). The coil occurs a changing current that creates an alternating magnetic field. Magnetic Flow Change F \u003d LI This field will excrete in the turns of the coil of EMF self-induction
.
Since the voltage belonging to the coil plays the role of EMF, and there is no voltage drop in the chain ( R. \u003d 0), according to the second Rule of Kirchhoff for instant values \u200b\u200bwe can write:
u. + \u003d 0 or 
.
Last rewrite in the form differential equation
Or 
.
The integration of this equation gives the following expression:
.
,
(35)
From (31) and (35) follows:
1) the current passing through the coil is lagging behind the phase voltage on P / 2 or that the same, the voltage is ahead of the current in phase per P / 2;
From comparison (36) C (32) it follows that the value of W L. In the circuit with inductance plays the role of resistance. Magnitude
X L.\u003d W. L. (37)
call inductive resistance.
Capacitance. The condenser is a rupture of wires, so it does not miss the constant current. When the voltage changes between the plates, the instantaneous value of the capacitor charge determined by the formula is changing
q \u003d Cu., (38)
for which in the supply wires should flow, bringing a charge to the folds or carrying away from them. It is said that the capacitor skips alternating current, although in the space between the plates there is no charge of charge from one plug to another.
Passing on the wires charge accumulates on the capacitor plates, so its value is equal i \u003d dq / dtwhere q. - Instant climbing value. Considering (38) and considering the supplied voltage varying by law (31), we obtain:
.
Since COS (P / 2 + W t.) \u003d -Sin W t, The latter will take the form:
. (39)
Comparing (31) and (39), we have:
1) the current in the circuit with the capacitor is ahead of the phase voltage on P / 2, in other words, the voltage is lagging behind the current on P / 2 phase;
2) current and voltage amplitudes are associated with relation
. (40)
Magnitude
call capacitive resistance.
When measuring and calculating alternating current circuits instead of amplitude use existing (effective) values \u200b\u200bof current strength I. and voltage U.related to amplitude:
Their use is due to the fact that the Joule-Lenza law in the case of AC makes the same appearance as for the permanent. Accordingly, electrical measuring devices are graded to effective values.
It is obvious that formulas (34), (36) and (40) do not change when replacing amplitude values \u200b\u200bto efficient and will take a look:
U r \u003d i × r, U L. = I.× W. L., U C. = I./ W. C., (42)
where indexes R., L.and C. Mean the voltage on the appropriate load.
Vector diagrams. Phase ratios between current and voltage are graphically shown in Fig. thirty.
There is another way of their presentation that allows you to simplify the calculations of the chains with a complex load.
 Fig. 31. |
Spend from some point ABOUT (Fig. 31) axis OH and postpone from the same point vector BUTat an angle j to the axis OH. Then we give this vector to rotate around the point. ABOUT In the plane of the pattern counterclockwise with an angular velocity w. Angle A Between A®.and OH After some time t.will be a \u003d w t. + j. Projection A®.on the axis OH equal
A H. = H. = A.cOS A.
H. = A.cOS (W. t. + j). (43)
Output: All harmonic oscillation It can be submitted to the rotation of the vector of the corresponding length and orientation.
Consequently, if you build a vector U. and under the appropriate angle to postpone the vector I., with joint ventilation vectors, the angle between them will remain unchanged (43). Vector current and voltage diagrams at various loads are shown in Fig. 32.
Serial connection R., L and S.. To calculate such a chain, we use the method of vector diagrams. With a serial connection of loads, the instantaneous value of the current for the current in all points of the chain should be the same, i.e. The current phase on all loads is the same.
However, stresses on loads do not coincide in phase with a current. The voltage on ohmic resistance coincides in phase with the current, on the inductive - ahead of the current on P / 2, on the capacitive - lags behind P / 2. Thus, folding vectors U R., U L. and U C., I get the total voltage applied to the chain. Insofar as U L. and U C.opposite to the direction, it is more convenient to first fold them and then vector U L - U C Clause S. U R.. As a result, we have:
.
Substituting relations (42), we get:
. (44)
In this expression, the role of resistance performs the magnitude
, (45)
called full chain resistance to the variable current or impedance. With its use (44) takes the form:
U \u003d I × Z. (46)
This expression is often called the law of OM for variable currents. Value
(47)
called reactive resistance and is a combination of inductive and capacitive resistance.
The vector diagram (Fig. 33) also shows that the applied voltage and the current flow fluctuates not in the same phase, but have shift phasesj, the value of which is determined by any of the formulas below following the diagram:
; 
;
.
It should be noted that formula (46) is general for any compound of loads, and formulas (45), (47) and (48) are valid only for a particular case of a serial connection.
experimental part
Equipment: Reostat 1000 Ohm, key, ammeter, voltmeter, periodate 100 ohms, capacitors battery, coil.
Procedure for performing work
Exercise 1. Measurement of ohmic resistance.
The installation scheme is shown in Fig. 34.
In this experience, a low-level retainer is applied as a load. High resistance is used as a potentiometer.
1. Measure the current through the load at three different values \u200b\u200bof the voltage supplied to it. Measurement results are table. 12.
Task 2. Measurement of capacitive resistance.
1. In the working scheme, as a load, turn on the capacitors battery. The current and voltage on the load measure the same way as a job 1. Measurement results are also added to Table. 12.
Note.The value of the battery capacity is recommended to select in the range of 20-40 microf.
Task 3. Measuring the impedance of the coil.
1. Measurement of the impedance of the coil is carried out similarly to previous tasks using the coil as a load.
Task 4. Measurement of the Impedance of the Serial Connection R, L and S.
1. The load will serve the connected deostat, the capacitor battery and the coil.
2. Current and voltage at the load measure the same way to task 1.
3. According to each measurement, calculate impedances Z. Expalted loads.
4. Compare experimental results with theoretical or passport values. The results of the comparison will lead in the output.
Table 12.
| Task number | Voltage, U. | Current force I. | Z. exp, Oh. | Z. ExpSR , Oh. | Z. Theorem, Om. | ||||
| value of division | in divisions | in B. | value of division | in divisions | in A. | ||||
| resistor | |||||||||
| capacitor | |||||||||
| coil | |||||||||
| 4 Serial connection | |||||||||
Note.The theoretical for the row will be its passport resistance value. For condenser Z. Theore is determined by the value used in the experiment, the calculation is calculated by formula (41). The coil possesses both ohmic and inductive resistance, therefore its impedance is calculated by formula (45), and as R. The sum of ohmic resistances of the risostat and coil should be used.
5. Calculating the errors of experimental values \u200b\u200bto produce the accuracy classes of the ammeter and voltmeter, theoretical - according to passport data of the instruments.
Check questions and tasks
1. Write down and explain the law of Oma for AC.
2. How is the ohmic, reactive and impedance in the AC circuit?
3. What is understood under the effective values \u200b\u200bof current and voltage?
4. Draw a vector diagram for the resistor in the AC circuit. Make explanations.
5. Draw a vector diagram for a capacitor in the AC circuit. Make explanations.
6. Draw the vector diagrams for the perfect coil and coils with a noticeable ohmic resistance in the AC circuit. Make explanations.
7. Draw a vector diagram for a sequential connection of the resistor, condenser and coils in the AC circuit. Make explanations. Get Ohm's law from the vector diagram.
Laboratory work 9 (11)
Measuring power
In alternating current circuit
Purpose: You can familiarize yourself with the measurement of the power in the variable current circuit by the method of three voltmeters.
Theoretical part
Like every conductor, the coil in the DC circuit consumes the energy running on the heating of the wires. Property of the conductor to convert electric current to thermal is characterized by its ohmic resistance R.. The power of heat losses is determined by the formula
where I. - Current power in the conductor.
When the coil is turned on to the AC chain, it also sends heat by law (49), but in this case I. - Effective value of the forces of alternating current.
If the coil has a ferromagnetic core, then an alternating current passing through the coil excites vortex currents in it (Foucault currents) leading to the heating of the core. In addition, there is a continuous change in the magnetization of the core in size and direction (reclamation), which also leads to the heating of the core. These additional energy losses are equivalent to increasing the resistance of the conductor. Cumulative irreversible energy losses that are on the heating of both wires and core are characterized. active resistance Coils defined by the formula
This resistance, in contrast to ohmic, cannot be measured, it can only be calculated.
The voltage drop on active resistance is considered to be fluid in phase with a current.
 Fig. 35. |
In the absence of a wattmeter, the power consumed by the coil can be determined using three voltmeters. If the coil has inductance L. and active resistance R. and then between the current in the coil and the voltage on it there is a shift of phases J, which is illustrated by a vector diagram (Fig. 35), where I. - Current through the coil, U. AI U L. - voltage drops on the active and inductive resistance of the coil, U. K - full voltage on the coil.
The power consumed power can be calculated either from (49) or by formula
. (51)
I. and U. It is measured directly, and to determine the power factor (COS J), an ohmic resistance is included in series with the coil R..
From the vector diagram (Fig. 36) The total voltage in the circuit is recorded by the cosine theorem:
. (52)
 Fig. 36. |
In these expressions U. - the supplied voltage, U. K - Voltage on the coil, U R. - Voltage on ohmic resistance. All three voltages are measurable directly. Next, since the coil and ohmic resistance is connected in series, the current of the current in them is the same and determined by the formula
what allows you to do without an ammeter.
experimental part
Equipment: autotransformer; coil; rheostat; Voltmeter 0-50 V; 2 voltmeter 0-150 V; Solid and typical cores.
Procedure for performing work
Exercise 1. Measuring the power of the coil without a core.
In the diagram in fig. 37 The voltage supplied to the chain is adjusted by the autotransformer. Reostat is used as ohmic resistance.
