Ohm's law on alternating current impedance. Ohm's law in simple terms

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Ohm's law

The figure shows a diagram of the simplest familiar to you electrical circuit. This closed circuit consists of three elements:

• voltage source – GB batteries;
• current consumer - load R, which can be, for example, a filament electric lamp or resistor;
• conductors connecting the voltage source to the load.

By the way, if this circuit is supplemented with a switch, it will turn out complete diagram pocket electric flashlight. The load R, which has a certain resistance, is a section of the circuit.

The value of the current in this section of the circuit depends on the voltage acting on it and its resistance: the higher the voltage and the lower the resistance, the greater the current will flow through the section of the circuit.

This dependence of current on voltage and resistance is expressed by the following formula:

• I – current, expressed in amperes, A;
• U – voltage in volts, V;
• R – resistance in ohms, Ohm.

This mathematical expression is read as follows: the current in a section of the circuit is directly proportional to the voltage across it and inversely proportional to its resistance. This is the basic law of electrical engineering, called Ohm's law (after G. Ohm's surname) for a section of an electrical circuit. Using Ohm's law, you can find out the unknown third from two known electrical quantities. Here are some examples practical application Ohm's law:

1. First example. A voltage of 25 V is applied to a section of the circuit with a resistance of 5 ohms. It is necessary to find out the value of the current in this section of the circuit. Solution: I = U/R = 25 / 5 = 5 A.
2. Second example. A voltage of 12 V acts on a section of the circuit, creating a current of 20 mA in it. What is the resistance of this section of the circuit? First of all, the current 20 mA must be expressed in amperes. This will be 0.02 A. Then R = 12 / 0.02 = 600 Ohms.
3. Third example. A current of 20 mA flows through a section of a circuit with a resistance of 10 kOhm. What is the voltage acting on this section of the circuit? Here, as in the previous example, the current must be expressed in amperes (20 mA = 0.02 A), resistance in ohms (10 kOhm = 10000 Ohms). Therefore, U = IR = 0.02×10000 = 200 V.

The incandescent lamp base of a flat flashlight is stamped with: 0.28 A and 3.5 V. What does this information mean? The fact that the light bulb will glow normally at a current of 0.28 A, which is determined by a voltage of 3.5 V. Using Ohm's law, it is easy to calculate that the heated filament of the light bulb has a resistance R = 3.5 / 0.28 = 12.5 Ohm .

This is the resistance of the heated filament of the light bulb; the resistance of the cooled filament is much less. Ohm's law is valid not only for a section, but also for the entire electrical circuit. In this case, the total resistance of all circuit elements, including internal resistance current source. However, in the simplest circuit calculations, the resistance of the connecting conductors and the internal resistance of the current source are usually neglected.

In this regard, it is necessary to give one more example: the voltage of the electric lighting network is 220 V. What current will flow in the circuit if the load resistance is 1000 Ohms? Solution: I = U/R = 220 / 1000 = 0.22 A. An electric soldering iron consumes approximately this current.

All these formulas, which follow from Ohm’s law, can also be used to calculate circuits AC, but provided that there are no inductors and capacitors in the circuits.

Ohm's law and the calculation formulas derived from it are quite easy to remember if you use this graphic diagram, this is the so-called Ohm's law triangle.

Using this triangle is easy, just remember clearly that horizontal line it means the division sign (similar to the fractional line), and the vertical line means the multiplication sign.

Now we should consider the following question: how does a resistor connected in the circuit in series with the load or in parallel to it affect the current? It's better to understand this with an example. There is a light bulb from a round electric flashlight, designed for a voltage of 2.5 V and a current of 0.075 A. Is it possible to power this light bulb from a 3336L battery, the initial voltage of which is 4.5 V?

It is easy to calculate that the heated filament of this light bulb has a resistance of slightly more than 30 ohms. If you power it from a fresh 3336L battery, then, according to Ohm’s law, a current will flow through the filament of the light bulb, almost twice the current for which it is designed. The thread will not withstand such an overload; it will overheat and collapse. But this light bulb can still be powered from a 336L battery if an additional 25 Ohm resistor is connected in series with the circuit.

In this case total resistance external circuit will be equal to approximately 55 Ohms, that is, 30 Ohms - the resistance of the light bulb filament H plus 25 Ohms - the resistance of the additional resistor R. Consequently, a current equal to approximately 0.08 A will flow in the circuit, that is, almost the same as that for which it is designed light bulb filament.

This light bulb can be powered from a battery and with more high voltage and even from the electric lighting network, if you select a resistor of appropriate resistance. In this example, an additional resistor limits the current in the circuit to the value we need. The greater its resistance, the less will be the current in the circuit. IN in this case two resistances were connected in series in the circuit: the resistance of the light bulb filament and the resistance of the resistor. And when serial connection resistance current is the same at all points of the circuit.

You can turn on the ammeter at any point, and it will show the same value everywhere. This phenomenon can be compared to the flow of water in a river. The river bed in different areas can be wide or narrow, deep or shallow. However, over a certain period of time, the same amount of water always passes through the cross section of any section of the river bed.

An additional resistor connected in series with the load can be considered as a resistor that “quenches” part of the voltage acting in the circuit. The voltage that is extinguished by the additional resistor, or, as they say, drops across it, will be greater, the greater the resistance of this resistor. Knowing the current and resistance of the additional resistor, the voltage drop across it can be easily calculated using the same familiar formula U = IR, here:

• U – voltage drop, V;
• I – current in the circuit, A;
• R – resistance of the additional resistor, Ohm.

In relation to the example, resistor R (see figure) extinguished the excess voltage: U = IR = 0.08 × 25 = 2 V. The remaining battery voltage, equal to approximately 2.5 V, fell on the light bulb filaments. The required resistor resistance can be found using another formula familiar to you: R = U/I, where:

• R – the required resistance of the additional resistor, Ohm;
• U – voltage that needs to be extinguished, V;
• I – current in the circuit, A.

For the example under consideration, the resistance of the additional resistor is: R = U/I = 2/0.075, 27 Ohm. By changing the resistance, you can decrease or increase the voltage that drops across the additional resistor, thus regulating the current in the circuit. But the additional resistor R in such a circuit can be variable, that is, a resistor whose resistance can be changed (see figure below).

In this case, using the resistor slider, you can smoothly change the voltage supplied to the load H, and therefore smoothly regulate the current flowing through this load. A variable resistor connected in this way is called a rheostat. Rheostats are used to regulate currents in the circuits of receivers, televisions and amplifiers. In many cinemas, rheostats were used to smoothly dim the light in the auditorium. There is another way to connect the load to a current source with excess voltage - also using variable resistor, but turned on by a potentiometer, that is, a voltage divider, as shown in the figure below.

Here R1 is a resistor connected by a potentiometer, and R2 is a load, which can be the same incandescent light bulb or some other device. A voltage drop occurs across resistor R1 of the current source, which can be partially or completely supplied to load R2. When the resistor slider is in its lowest position, no voltage is supplied to the load at all (if it is a light bulb, it will not light up).

As the resistor slider moves up, we will apply more and more voltage to the load R2 (if it is a light bulb, its filament will glow). When the slider of resistor R1 is in the uppermost position, the entire voltage of the current source will be applied to the load R2 (if R2 is a flashlight bulb, and the voltage of the current source is high, the light bulb filament will burn out). You can experimentally find the position of the variable resistor motor at which the voltage it needs will be supplied to the load.

Variable resistors activated by potentiometers are widely used to control volume in receivers and amplifiers. The resistor can be directly connected in parallel with the load. In this case, the current in this section of the circuit branches and goes in two parallel paths: through the additional resistor and the main load. Maximum current will be in the branch with the least resistance.

The sum of the currents of both branches will be equal to the current spent on powering the external circuit. TO parallel connection are used in those cases when it is necessary to limit the current not in the entire circuit, as when connecting an additional resistor in series, but only in a certain section. Additional resistors are connected, for example, in parallel with milliammeters, so that they can measure large currents. Such resistors are called shunts or shunts. The word shunt means a branch.

Ohm's law was discovered by the German physicist Georg Ohm in 1826 and has since been widely used in the electrical field in theory and practice. It is expressed by a well-known formula, with which you can perform calculations on almost any electrical circuit. However, Ohm's law for alternating current has its own characteristics and differences from connections with DC, determined by the presence of reactive elements. To understand the essence of its work, you need to go through the entire chain, from simple to complex, starting with a separate section of the electrical circuit.

Ohm's law for a circuit section

Ohm's law is considered to work for various options electrical circuits. It is best known by the formula I = U/R, applied to a separate section of a direct or alternating current circuit.

It contains definitions such as current (I), measured in amperes, voltage (U), measured in volts, and resistance (R), measured in ohms.

The widely accepted definition of this formula is expressed by the well-known concept: the current strength is directly proportional to the voltage and inversely proportional to the resistance on a specific section of the circuit. If the voltage increases, then the current increases, and an increase in resistance, on the contrary, reduces the current. The resistance on this segment can consist not only of one, but also of several elements connected to each other.

The formula for Ohm's law for direct current can be easily remembered using the special triangle shown in the general figure. It is divided into three sections, each of which contains a separate parameter. This hint makes it possible to quickly and easily find the desired value. The required indicator is covered with a finger, and actions with the remaining ones are performed depending on their position relative to each other.

If they are located on the same level, then they need to be multiplied, and if they are on different levels, the upper parameter is divided by the lower one. This method will help beginner electrical engineers avoid confusion in calculations.

Ohm's law for a complete circuit

There are certain differences between a section and a whole chain. A section or segment is considered to be a part of the general circuit located in the current or voltage source itself. It consists of one or more elements connected to a current source in different ways.

The complete chain system is general scheme, consisting of several chains, including batteries, different types loads and the wires connecting them. It also works according to Ohm's law and is widely used in practice, including for alternating current.

The principle of operation of Ohm's law in a complete DC circuit can be clearly seen by performing a simple experiment. As the figure shows, this will require a current source with voltage U at its electrodes, any constant resistance R and connecting wires. As resistance you can take an ordinary lamp incandescent A current will flow through its filament, created by electrons moving inside metal conductor, in accordance with the formula I = U/R.

System common circuit will consist of an outer section, including resistance, connecting wires and battery contacts, and an inner section located between the electrodes of the current source. A current formed by ions with positive and negative charges will also flow through the internal section. The cathode and anode will begin to accumulate charges with plus and minus, after which a charge will appear among them.

The full movement of ions will be hampered by the internal resistance of the battery r, which limits the output of current to the external circuit and reduces its power to a certain limit. Consequently, the current in the common circuit passes within the internal and external circuits, alternately overcoming the total resistance of the segments (R+r). The size of the current is influenced by such a concept as electromotive force - EMF applied to the electrodes, indicated by the symbol E.

The EMF value can be measured at the battery terminals using a voltmeter with the external circuit turned off. After connecting the load, the presence of voltage U will appear on the voltmeter. Thus, when the load is disconnected, U = E, when connecting the external circuit U< E.

EMF gives impetus to the movement of charges in a complete circuit and determines the current strength I = E/(R+r). This formula reflects Ohm's law for a complete DC electrical circuit. It clearly shows the signs of internal and external contours. If the load is disconnected, charged particles will still move inside the battery. This phenomenon is called self-discharge current, leading to unnecessary consumption of metal particles in the cathode.

Under the influence of the internal energy of the power source, the resistance causes heating and its further dissipation outside the element. Gradually, the battery charge completely disappears without a trace.

Ohm's law for an alternating current circuit

For AC circuits, Ohm's law will look different. If we take the formula I = U/R as a basis, then in addition to the active resistance R, inductive XL and capacitive XC resistances, which are classified as reactive, are added to it. Similar electrical diagrams are used much more often than connections with only active resistance and allow you to calculate any options.

This also includes the parameter ω, which is the cyclic frequency of the network. Its value is determined by the formula ω = 2πf, in which f is the frequency of this network (Hz). At constant current, this frequency will be equal to zero, and the capacitance will take an infinite value. In this case, the DC electrical circuit will be broken, that is, there is no reactance.

An alternating current circuit is no different from a direct current circuit, with the exception of the voltage source. The general formula remains the same, but when reactive elements are added, its content will completely change. The parameter f will no longer be zero, which indicates the presence of reactance. It also affects the current flowing in the circuit and causes resonance. The symbol Z is used to indicate loop impedance.

The marked value will not be equal to the active resistance, that is, Z ≠ R. Ohm's law for alternating current will now look like the formula I = U/Z. Knowledge of these features and correct use formulas that will help avoid wrong decision electrical tasks and prevent failure individual elements contour.

Alternating electric current. Ohm's law.

AC, AC alternating current- alternating current) is an electric current that periodically changes in magnitude and direction.

Alternating current also refers to current in conventional single- and three-phase networks. In this case, the instantaneous values ​​of current and voltage change according to a harmonic law.

In DC consuming devices, AC current is often converted by rectifiers to produce DC current.

Ohm's law for alternating current generally has the same form as for direct current. That is, as the voltage in the circuit increases, the current in it will also increase. The difference is that in an alternating current circuit resistance is provided by elements such as an inductor and capacitance. Taking this fact into account, let us write down Ohm's law for alternating current.

Formula 1 - Ohm's law for alternating current

where z is impedance chains.

Formula 2 - circuit impedance

In general, the impedance of an alternating current circuit will consist of active capacitive and inductive reactance. Simply put, the current in an alternating current circuit depends not only on the active ohmic resistance, but also on the value of capacitance and inductance.

Figure 1 - circuit containing ohmic inductive and capacitance

If, for example, a capacitor is connected to a DC circuit, then there will be no current in the circuit, since a DC capacitor is an open circuit. If inductance appears in the DC circuit, the current will not change. Strictly speaking, it will change, since the coil will have ohmic resistance. But the change will be negligible. If the capacitor and coil are connected in an alternating current circuit, then they will resist the current in proportion to the value of the capacitance and inductance, respectively. In addition, a phase shift between voltage and current will be observed in the circuit. In general, the current in a capacitor leads the voltage by 90 degrees. In inductance it lags by 90 degrees. Capacitance depends on the size of the capacitance and the frequency of the alternating current. This dependence is inversely proportional, that is, with increasing frequency and capacitance, the resistance will decrease.

Formula 3 - capacitance

Inductive reactance is directly proportional to frequency and inductance. The greater the inductance and frequency, the greater the resistance to alternating current a given coil will provide.

Electric current, like any process, obeys the laws of physics. The famous German physicist Georg Simon Ohm, after whom the unit of measurement of resistance is named, in 1826 empirically derived formulas relating current, voltage and resistance. Initially, the law aroused distrust and criticism in scientific circles. Then the correctness of his reasoning was confirmed by the Frenchman Claude Poulier, and Ohm’s works received well-deserved recognition.

Ohm's law for an electric circuit (complete)

Special case – Ohm's law for a circuit section:

Let's add to these formulas electrical power, released during the passage of current:

The result is a series of formulas that are derived mathematically. They connect all of the listed physical quantities with each other.

Voltage	Current	Resistance	Power

Electromotive force and internal resistance

Electromotive force of voltage source characterizes its ability to provide a constant potential difference at the terminals. This force is of a non-electrical nature: chemical in batteries, mechanical in generators.

What is the role of the internal resistance of the power supply and what is it? Let's say you short-circuited the leads car battery small cross-section copper conductor. IN physical sense you connected a resistance close to zero to a DC source. If we use the formula for a section of a circuit, then an infinitely large current should flow through the battery and the wire. This doesn't actually happen, but the wire will burn.

Now let's connect the battery with the same wire. Less current will flow through it. This is due to the internal resistance being higher than that of a battery. At low load resistance, the law formula for a complete circuit becomes

As a result, the current through a short-circuited battery will have a finite value, and the power will lead to heating of the battery. If we shorted the battery with a thicker wire that could withstand the current short circuit, then it would noticeably heat the source from the inside.

E.M.S. source can be measured with some accuracy with a voltmeter with high input impedance. The internal resistance of the source cannot be measured directly, but only calculated.

Georg Simon Ohm began his research inspired by the famous work of Jean Baptiste Fourier, “The Analytical Theory of Heat.” In this work, Fourier represented the heat flow between two points as a temperature difference, and associated the change in heat flow with its passage through an irregularly shaped obstacle made of heat-insulating material. Similarly, Om caused the emergence electric current potential difference.

Based on this, Om began to experiment with different materials conductor. In order to determine their conductivity, he connected them in series and adjusted their length so that the current strength was the same in all cases.

It was important for such measurements to select conductors of the same diameter. Ohm, measuring the conductivity of silver and gold, obtained results that, according to modern data, are not accurate. Thus, Ohm's silver conductor conducted less electric current than gold. Om himself explained this by saying that his silver conductor was coated with oil and because of this, apparently, the experiment did not give accurate results.

However, this was not the only problem that physicists who at that time were engaged in similar experiments with electricity had problems with. Great difficulties in obtaining pure materials without impurities for experiments and difficulties in calibrating the diameter of the conductor distorted the test results. An even bigger snag was that the current strength was constantly changing during the tests, since the current source was variable chemical elements. Under such conditions, Ohm derived a logarithmic dependence of the current on the resistance of the wire.

A little later, the German physicist Poggendorff, who specialized in electrochemistry, suggested that Ohm replace the chemical elements with a thermocouple made of bismuth and copper. Om began his experiments again. This time he used a thermoelectric device powered by the Seebeck effect as a battery. To it he connected in series 8 copper conductors of the same diameter, but of different lengths. To measure the current, Ohm suspended a magnetic needle over the conductors using a metal thread. The current running parallel to this arrow shifted it to the side. When this happened, the physicist twisted the thread until the arrow returned to starting position. Based on the angle at which the thread was twisted, one could judge the value of the current.

As a result of a new experiment, Ohm came to the formula:

X = a / b + l

Here X– intensity magnetic field wires, l– wire length, a – constant source voltage, b – resistance constant the remaining elements of the chain.

If you turn to modern terms to describe this formula, we get that X– current strength, A – EMF source, b + l– total circuit resistance.

Ohm's law for a circuit section

Ohm's law for a separate section of a circuit states: the current strength in a section of a circuit increases as the voltage increases and decreases as the resistance of this section increases.

I=U/R

Based on this formula, we can decide that the resistance of the conductor depends on the potential difference. From a mathematical point of view, this is correct, but from a physics point of view, it is false. This formula is only applicable for calculating resistance at separate area chains.

Thus, the formula for calculating the conductor resistance will take the form:

R = p ⋅ l / s

Ohm's law for a complete circuit

The difference between Ohm's law for a complete circuit and Ohm's law for a section of a circuit is that now we must take into account two types of resistance. This is “R” the resistance of all system components and “r” the internal resistance of the source electromotive force. The formula thus takes the form:

I = U / R + r

Ohm's law for alternating current

Alternating current differs from direct current in that it changes over certain time periods. Specifically, it changes its meaning and direction. To apply Ohm's law here, you need to take into account that the resistance in a circuit with direct current may differ from the resistance in a circuit with alternating current. And it differs if components with reactance are used in the circuit. Reactance can be inductive (coils, transformers, chokes) or capacitive (capacitor).

Let's try to figure out what real difference between reactive and active resistance in a circuit with alternating current. You should already understand that the value of voltage and current in such a circuit changes over time and, roughly speaking, have a wave form.

If we diagram how these two values ​​change over time, we get a sine wave. Both voltage and current rise from zero to maximum value, then, descending, pass through the zero value and reach the maximum negative value. After this, they rise again through zero to the maximum value and so on. When it is said that current or voltage is negative, it means that it moves in the opposite direction.

The whole process occurs with a certain frequency. The point where the voltage or current value from minimum value rising to the maximum value and passing through zero is called phase.

In fact, this is just a preface. Let's return to reactive and active resistance. The difference is that in a circuit with active resistance, the current phase coincides with the voltage phase. That is, both the current value and the voltage value reach a maximum in one direction at the same time. In this case, our formula for calculating voltage, resistance or current does not change.

If the circuit contains reactance, the phases of the current and voltage shift from each other by ¼ of a period. This means that when the current reaches its maximum value, the voltage will be zero and vice versa. When to use inductive reactance, the voltage phase “overtakes” the current phase. When capacitance is applied, the current phase "overtakes" the voltage phase.

Formula for calculating the voltage drop across inductive reactance:

U = I ⋅ ωL

Where L is the inductance of the reactance, and ω – angular frequency (time derivative of the oscillation phase).

Formula for calculating the voltage drop across capacitance:

U = I / ω ⋅ C

WITH– reactance capacitance.

These two formulas are special cases of Ohm's law for variable circuits.

The complete one will look like this:

I=U/Z

Here Z– total resistance variable circuit known as impedance.

Scope of application

Ohm's law is not a basic law in physics, it is just a convenient dependence of some values ​​on others, which is suitable in almost any practical situation. Therefore, it will be easier to list situations when the law may not work:

• If there is inertia of charge carriers, for example in some high-frequency electric fields;
• In superconductors;
• If the wire heats up to such an extent that the current-voltage characteristic ceases to be linear. For example, in incandescent lamps;
• In vacuum and gas radio tubes;
• In diodes and transistors.