What is Ohm's law for a complete chain? So, this is a formula in which the connection between the main parameters of an electrical circuit is clearly visible: current, voltage and resistance. In order to understand the essence of the law, let's first understand some of the concepts.
What is called an electrical circuit?
An electrical circuit is a path in an electrical circuit through which charges (electrical elements, wires, and other devices) flow. Of course, the power source is considered to be its beginning. Under the influence of an electromagnetic field, photonic phenomena or chemical processes, electric charges tend to move to the opposite terminal of this power source.
What is Electric Current?
The directional movement of charged particles when exposed to an electric field or other external forces is called electric current. Its direction is determined by the directionality of the protons (positive charges). The current will be constant if over time neither its strength nor direction has changed.
Ohm's Law History
When conducting experiments with a conductor, physicist Georg Ohm was able to establish that the current strength is proportional to the voltage that is applied to its ends:
I / sim U or I = G / U,
where G is the electrical conductivity, and the value R = 1 / G is the electrical resistance of the conductor. This discovery was established by the famous German physicist in 1827.
Ohm's laws
For a complete circuit, the definition will be as follows: the current in the circuit is equal to the ratio of the electromotive force (hereinafter EMF) of the source to the sum of the resistances:
I = E / (R + r),
where R is the resistance of the external circuit, and r is the internal resistance Quite often, the formulation of the law causes difficulties, since not everyone is familiar with the concept of EMF, its difference from voltage, not everyone knows what internal resistance means and where does it come from. For this, explanations are needed, because Ohm's law for a complete chain has a deep meaning.
The wording of the law for a section of the chain can be called transparent. The point is that no additional explanations are needed to understand it: the current in the circuit is directly proportional to the voltage and inversely proportional to the resistance:
Meaning
Ohm's law for a complete circuit is closely related to the law of conservation of energy. Let's assume that the current source has no internal resistance. What, then, should happen? It turns out that if there were no resistance, then a greater current would be given to the external circuit, and accordingly the power would be greater.
Now it's time to figure out the concept of electromotive force. This value is the difference between the electric potentials at the terminals of the source, but only without any load. Let's take the water pressure in a raised tank as an example. The water level will remain in place until it is consumed. When the tap is opened, the liquid level will decrease, since there is no pumping. Getting into the pipe, the water experiences resistance, the same thing happens with the electric charges in the wire.
In the absence of loads, the terminals are in an open state, it turns out that the EMF and voltage are the same in magnitude. If we, for example, turn on a light bulb, the circuit will close, and the electromotive force will create a voltage in it, doing useful work. Some of the energy will dissipate due to internal resistance (this is called loss).
In the event that the consumer's resistance is less than the internal one, then a large power is released at the current source. And then there is a drop in the EMF in the external circuit, and a significant part of the energy is lost on the internal resistance. The essence of conservation laws is that nature cannot take more than it gives.
The essence of internal resistance is well known to the inhabitants of "Khrushchevs", who have air conditioners in their apartments, and the old wiring has not been replaced. The electric meter rotates at a breakneck speed, the outlet and the wall heats up in those places where the old aluminum wires pass, as a result of which the air conditioner barely cools the air in the room.
Nature r
"Full Ohm" (as electricians are accustomed to calling the law) is poorly understood, since the internal resistance of the source, as a rule, is not electrical in nature. Let's look at this with a salt battery as an example. It is known that an electric battery consists of several elements, but we will consider only one. So, we have a ready-made battery "Krona", consisting of 7 series-connected cells.
How does the current generation take place? In a vessel with electrolyte, we place a carbon rod in a manganese sheath, consisting of positive electrodes or anodes. Specifically in this example, the carbon rod acts as a current collector. Zinc metal is made up of negative electrodes (cathodes). Commercial batteries usually contain gel electrolyte. Liquid is used very rarely. A zinc cup with electrolyte and anodes acts as a negative electrode.
It turns out that the secret of the battery lies in the fact that manganese's electric potential is not as high as that of zinc. Therefore, electrons are attracted to the cathode, which, in turn, repels positively charged zinc ions to the anode. As a result, the cathode is gradually consumed. Perhaps everyone knows that if a dead battery is not replaced in a timely manner, it may leak. What is the reason for this? Everything is very simple: electrolyte will start to flow through the disconnected glass.
When charges move on a carbon rod, positive charges accumulate in the manganese shell, while negative charges are collected on zinc. Therefore, they are called anode and cathode, but inside the batteries they look different. The difference between the charges will create an electromotive force. The charges will stop moving in the electrolyte when the potential difference of the electrode material is equal to the value of the EMF, and the attraction forces are equal to the repulsive forces.
Let's close the circuit now: all you need to do is connect the light bulb to the battery. Passing through an artificial light source, each charge will return to its place ("home"), and the light bulb will light up. Inside the battery, the movement of electrons and ions will begin again, since the charges have gone out, and an attractive or repulsive force reappeared.
In fact, the battery generates a current, which is why the light bulb glows, this is due to the consumption of zinc, which is converted in this process into other chemical compounds. To extract pure zinc, according to the law of conservation of energy, you need to spend it, but not in electrical form (exactly the same amount as was given to the light bulb).
Now we can finally figure out the nature of the internal resistance of the source. In a battery, this is an obstacle to the movement of large ions. The movement of electrons without ions is impossible, because there is no attraction force.
In industrial generators, r appears not only due to the electrical resistance of the windings, but also due to external causes. So, for example, in hydroelectric power plants, the value of the quantity depends on the efficiency of the turbine, the resistance of the water flow in the water conduit, and also on the losses in the mechanical transmission. In addition, the temperature of the water and how silt it is has some influence.
Alternating current
We have already considered Ohm's law for the entire circuit for direct current. How will the formula change with alternating current? Before we know that, let's characterize the concept itself. Alternating current is the movement of electrically charged particles, the direction and value of which changes over time. Unlike constant, it is accompanied by additional factors that give rise to a new type of resistance (reactive). It is characteristic of capacitors and inductors.
Ohm's law for a complete circuit for alternating current is:
where Z - complex resistance, consisting of active and reactive.
It's not all bad
Ohm's law for a complete circuit, in addition to indicating energy losses, also suggests ways to eliminate them. Ordinary electricians rarely use the formula for finding the complex resistance when there are capacitors or inductors in the circuit. In most cases, the current is measured with a clamp or a special tester. And when you know the voltage, you can easily calculate the complex resistance (if really necessary).
Let's assemble an electrical circuit (Figure 1, a) consisting of a battery 1 voltage of 2 V, lever rheostat 2 , two measuring instruments - voltmeter 3 and ammeter 4 and connecting wires 5 ... We set a resistance equal to 2 ohms in the circuit using a rheostat. Then a voltmeter connected to the battery terminals will show a voltage of 2 V, and an ammeter connected in series to the circuit will show a current equal to 1 A. Let's increase the voltage to 4 V by switching on another battery (Figure 1, b). With the same resistance in the circuit - 2 Ohm - the ammeter will already show a current of 2 A. A 6 V battery will change the ammeter reading to 3 A (Figure 1, v). Let's summarize our observations in Table 1.
Figure 1. Changing the current in an electrical circuit by changing the voltage with a constant resistance
Table 1
Dependence of the current in the circuit on the voltage with a constant resistance
From this we can conclude that the current in the circuit at a constant resistance is the greater, the greater the voltage of this circuit, and the current will increase as many times as the voltage increases.
Now, in the same circuit, we put a battery with a voltage of 2 V and use a rheostat to set the resistance in the circuit equal to 1 Ohm (Figure 2, a). Then the ammeter will show 2 A. b). The ammeter reading (at the same circuit voltage) will already be 1 A.
Figure 2. Changing the current in an electrical circuit by changing the resistance at a constant voltage
With a resistance in the circuit of 3 Ohm (Figure 2, v) the ammeter reading will be 2/3 A.
The result of the experiment is summarized in Table 2.
table 2
Dependence of the current in the circuit on the resistance at a constant voltage
From this it follows that at a constant voltage, the current in the circuit will be the greater, the lower the resistance of this circuit, and the current in the circuit increases as many times as the resistance of the circuit decreases.
Experiments show that the current in a section of the circuit is directly proportional to the voltage in this section and inversely proportional to the resistance of the same section. This relationship is known as Ohm's law.
If we denote: I- current in amperes; U- voltage in volts; r- resistance in ohms, then Ohm's law can be represented by the formula:
that is, the current in a given section of the circuit is equal to the voltage in this section divided by the resistance of the same section.
Video 1. Ohm's law for a chain section
Example 1. Determine the current that will flow through the filament of an incandescent lamp if the filament has a constant resistance of 240 ohms, and the lamp is connected to a network with a voltage of 120 V.
Using the Ohm's law formula, you can also determine the voltage and resistance of the circuit.
U = I × r ,
that is, the voltage of the circuit is equal to the product of the current and the resistance of this circuit and
that is, the resistance of the circuit is equal to the voltage divided by the current in the circuit.
Example 2. What voltage is needed for a current of 20 A to flow in a circuit with a resistance of 6 ohms?
U = I × r= 20 × 6 = 120 V.
Example 3. A current of 5 A flows along the spiral of the electric hotplate. The tile is connected to a network with a voltage of 220 V. Determine the resistance of the spiral of the electric hotplate.
If in the formula U = I × r current is 1 A, and the resistance is 1 Ohm, then the voltage will be 1 V:
1 V = 1 A × 1 Ohm.
Hence we conclude: a voltage of 1 V acts in a circuit with a resistance of 1 Ohm at a current of 1 A.
Voltage loss
Figure 3 shows an electrical circuit consisting of a battery, resistance r and long connecting wires that have their own specific resistance.
As can be seen from Figure 3, the voltmeter connected to the battery terminals shows 2 V. Already in the middle of the line, the voltmeter shows only 1.9 V, and near the resistance r the voltage is only 1.8 V. This decrease in voltage along the circuit between the individual points of this circuit is called voltage loss (drop).
Voltage loss along an electrical circuit occurs because a portion of the applied voltage is expended to overcome the circuit resistance. In this case, the voltage loss in a section of the circuit will be the greater, the greater the current and the greater the resistance of this section of the circuit. From Ohm's law for a section of a circuit, it follows that the voltage loss in volts in a section of a circuit is equal to the current in amperes flowing through this section, multiplied by the resistance in ohms of the same section:
U = I × r .
Example 4. From the generator, the voltage at the terminals of which is 115 V, electricity is transmitted to the electric motor through wires, the resistance of which is 0.1 Ohm. Determine the voltage at the terminals of the motor if it consumes a current of 50 A.
Obviously, the voltage at the terminals of the motor will be less than at the terminals of the generator, since there will be a voltage loss in the line. According to the formula, we determine that the voltage loss is equal to:
U = I × r= 50 × 0.1 = 5 V.
If the voltage loss in the line is 5 V, then the voltage of the electric motor will be 115 - 5 = 110 V.
Example 5. The generator gives a voltage of 240 V. Electricity is transmitted through a line of two copper wires 350 m long, with a cross section of 10 mm² to an electric motor that consumes a current of 15 A. It is required to know the voltage at the motor terminals.
The voltage at the motor terminals will be less than the generator voltage by the amount of voltage loss in the line. Line voltage loss U = I × r.
Since the resistance r wires are unknown, we determine it by the formula:
"); length l equal to 700 m, since the current has to go from the generator to the engine and from there back to the generator.
Substituting r into the formula, we get:
U = I × r= 15 x 1.22 = 18.3 V
Therefore, the voltage at the motor terminals will be 240 - 18.3 = 221.7 V
Example 6. Determine the cross-section of the aluminum wires that must be used to supply electrical energy to the engine operating at 120 V and 20 A. Power will be supplied to the engine from a 127 V generator along a 150 m line.
Find the permissible voltage loss:
127 - 120 = 7 V.
The resistance of the line wires must be equal to:
From the formula
determine the cross-section of the wire:
where ρ is the resistivity of aluminum (table 1, in the article "Electrical resistance and conductivity").
According to the reference book, we select the available cross-section of 25 mm².
If the same line is made with copper wire, then its cross-section will be equal to:
where ρ is the resistivity of copper (table 1, in the article "Electrical resistance and conductivity").
We choose a section of 16 mm².
Note also that sometimes it is necessary to deliberately achieve voltage loss in order to reduce the magnitude of the applied voltage.
Example 7. For stable burning of an electric arc, a current of 10 A is required at a voltage of 40 V. Determine the value of the additional resistance that must be connected in series with the arc installation in order to power it from a network with a voltage of 120 V.
The voltage loss in the additional resistance will be:
120 - 40 = 80 V.
Knowing the voltage loss in the additional resistance and the current flowing through it, it is possible, according to Ohm's law, for a section of the circuit to determine the value of this resistance:
When considering an electrical circuit, we have not yet taken into account the fact that the path of the current passes not only through the outer part of the circuit, but also through the inner part of the circuit, inside the element itself, a battery or other voltage source.
The electric current, passing through the inner part of the circuit, overcomes its internal resistance, and therefore a voltage drop also occurs inside the voltage source.
Consequently, the electromotive force (emf) of the source of electrical energy goes to cover the internal and external voltage losses in the circuit.
If we denote E- electromotive force in volts, I- current in amperes, r- resistance of the external circuit in ohms, r 0 - resistance of the internal circuit in ohms, U 0 - internal voltage drop and U Is the external voltage drop of the circuit, then we get that
E = U 0 + U = I × r 0 + I × r = I × ( r 0 + r),
This is the Ohm's law formula for the entire (complete) chain. In words, it reads like this: the current in an electrical circuit is equal to the electromotive force divided by the resistance of the entire circuit(the sum of internal and external resistance).
Video 2. Ohm's law for a complete circuit
Example 8. Electromotive force E element is equal to 1.5 V, its internal resistance r 0 = 0.3 ohm. The element is closed to resistance r= 2.7 ohms. Determine the current in the circuit.
Example 9. Determine e. etc. with. element E closed on resistance r= 2 Ohm, if the current in the circuit I= 0.6 A. Internal resistance of the element r 0 = 0.5 ohm.
A voltmeter connected to the terminals of the element will show the voltage across them, equal to the mains voltage or the voltage drop in the external circuit.
U = I × r= 0.6 × 2 = 1.2 V.
Therefore, part of e. etc. with. element goes to cover internal losses, and the rest - 1.2 V is given to the network.
Internal voltage drop
U 0 = I × r 0 = 0.6 x 0.5 = 0.3 V.
Because E = U 0 + U, then
E= 0.3 + 1.2 = 1.5V
The same answer can be obtained by using the Ohm's law formula for a complete circuit:
E = I × ( r 0 + r) = 0.6 × (0.5 + 2) = 1.5 V.
A voltmeter connected to the terminals of any power source. etc. with. during its operation, it shows the voltage on them or the voltage of the network. When the electrical circuit is opened, the current will not pass through it. The current will not pass also inside the source of e. etc., and therefore there will be no internal voltage drop. Therefore, the voltmeter with an open circuit will show e. etc. with. source of electrical energy.
Thus, the voltmeter connected to the terminals of the e. etc. with. shows:
a) with a closed electric circuit - mains voltage;
b) with an open electrical circuit - e. etc. with. source of electrical energy.
Example 10. The electromotive force of the element is 1.8 V. It is closed to resistance r= 2.7 ohms. The current in the circuit is 0.5 A. Determine the internal resistance r 0 elements and internal voltage drop U 0 .
Because r= 2.7 Ohm, then
r 0 = 3.6 - 2.7 = 0.9 ohm;
U 0 = I × r 0 = 0.5 x 0.9 = 0.45 V.
From the solved examples, it can be seen that the reading of the voltmeter connected to the terminals of the power source. etc., does not remain constant under various operating conditions of the electrical circuit. As the current in the circuit increases, the internal voltage drop also increases. Therefore, with a constant e. etc. with. the share of the external network will have less and less voltage.
Table 3 shows how the voltage of the electrical circuit changes ( U) depending on the change in external resistance ( r) with constant e. etc. with. ( E) and internal resistance ( r 0) energy source.
Table 3
Dependence of circuit voltage on resistance r with constant e. etc. with. and internal resistance r 0
| E | r 0 | r | U 0 = I × r 0 | U = I × r | |
| 2 2 2 | 0,5 0,5 0,5 | 2 1 0,5 | 0,8 1,33 2 | 0,4 0,67 1 | 1,6 1,33 1 |
Such as electric current, voltage, resistance and power. It was the turn of the basic electrical laws, so to speak, the basis, without the knowledge and understanding of which it is impossible to study and understand electronic circuits and devices.
Ohm's law
Electric current, voltage, resistance and power are certainly related. And the relationship between them is described, without a doubt, by the most important electrical law - Ohm's law... In a simplified form, this law is called: Ohm's law for a section of a chain. And this law sounds like this:
"The strength of the current in a section of the circuit is directly proportional to the voltage and inversely proportional to the electrical resistance of this section of the circuit."
For practical application, the Ohm's law formula can be represented in the form of such a triangle, which, in addition to the basic representation of the formula, will help determine the rest of the quantities.
The triangle works as follows. To calculate one of the quantities, it is enough to close it with your finger. For instance:
In the previous article, we drew an analogy between electricity and water, and identified the relationship between voltage, current and resistance. Also, the following figure can serve as a good interpretation of Ohm's law, which clearly displays the essence of the law:
On it we see that the man "Volt" (voltage) pushes the man "Ampere" (current) through the conductor, which pulls together the man "Om" (resistance). So it turns out that the stronger the resistance compresses the conductor, the harder it is for the current to pass through it ("the current strength is inversely proportional to the resistance of the circuit section" - or the greater the resistance, the worse the current falls and the less it is). But the voltage does not sleep and pushes the current with all its might (the higher the voltage, the greater the current or - "the current in the circuit section is directly proportional to the voltage").
When the flashlight starts to shine faintly, we say - "the battery is discharged." What happened to her, what does it mean she is discharged? This means that the battery voltage has decreased and it is no longer able to "help" the current to overcome the resistance of the flashlight and light bulb circuits. So it turns out that the higher the voltage, the higher the current.
Serial connection - serial circuit
When consumers are connected in series, for example, ordinary light bulbs, the current strength in each consumer is the same, but the voltage will be different. At each of the consumers, the voltage will drop (decrease).
And Ohm's law in a series circuit will look like:
With a series connection, the resistances of the consumers add up. Formula for calculating total resistance:
Parallel connection - parallel circuit
When connected in parallel, the same voltage is applied to each consumer, but the current through each of the consumers, if their resistance is different, will be different.
Ohm's law for a parallel circuit consisting of three consumers will look like:
When connected in parallel, the total resistance of the circuit will always be less than the value of the smallest individual resistance. Or they also say that "the resistance will be less than the smallest one."
The total resistance of a circuit consisting of two consumers in parallel connection:
The total resistance of a circuit consisting of three consumers in parallel connection:
For a larger number of consumers, the calculation is based on the fact that with a parallel connection, the conductivity (the reciprocal of resistance) is calculated as the sum of the conductivities of each consumer.
Electric power
Power is a physical quantity that characterizes the rate of transmission or conversion of electrical energy. The power is calculated using the following formula:
Thus, knowing the voltage of the source and measuring the current consumption, we can determine the power consumed by the electrical appliance. And vice versa, knowing the power of the appliance and the mains voltage, we can determine the amount of current consumed. Such calculations are sometimes necessary. For example, fuses or circuit breakers are used to protect electrical appliances. To choose the right protective device, you need to know the current consumption. Fuses used in household appliances, as a rule, must be repaired and it is enough to restore them.
One of the most widely used laws in electrical engineering. This law reveals the connection between the three most important quantities: current strength, voltage and resistance. This connection was revealed by Georg Ohm in the 1820s, which is why this law received such a name.
Ohm's law wording next:
The magnitude of the current in a section of the circuit is directly proportional to the voltage applied to this section, and inversely proportional to its resistance.
This dependence can be expressed by the formula:
Where I is the current strength, U is the voltage applied to the section of the circuit, and R is the electrical resistance of the section of the circuit.
So, if you know two of these quantities, you can easily calculate the third.
Ohm's law can be understood using a simple example. Let's say we need to calculate the resistance of the incandescent filament of a light bulb to a flashlight and we know the voltage values of the light bulb and the current required for its operation (the light bulb itself, so that you know, has a variable resistance, but for an example, we will take it as constant). To calculate the resistance, the voltage must be divided by the current strength. How to remember the Ohm's law formula in order to carry out the calculations correctly? And it's very easy to do it! You just need to make yourself a reminder like in the picture below.
Now, covering any of the quantities with your hand, you will immediately understand how to find it. If you close the letter I, it becomes clear that in order to find the current strength, you need to divide the voltage by resistance.
Now let's figure out what the words “directly proportional and inversely proportional to” mean in the formulation of the law. The expression "the magnitude of the current in the section of the circuit is directly proportional to the voltage applied to this section" means that if the voltage in the section of the circuit increases, then the current in this section will also increase. In simple words, the higher the voltage, the higher the current. And the expression "is inversely proportional to its resistance" means that the greater the resistance, the less the current will be.
Consider an example of how a light bulb works in a flashlight. Let's say that the flashlight needs three batteries, as shown in the diagram below, where GB1 - GB3 are batteries, S1 is a switch, HL1 is a light bulb.
Let us assume that the resistance of the light bulb is conditionally constant, although its resistance increases as it heats up. The brightness of the light bulb will depend on the strength of the current, the more it is, the brighter the light bulb burns. Now, imagine that instead of one battery, we inserted a jumper, thereby reducing the voltage.
What will happen to the light bulb?
It will shine more dimly (the current has decreased), which confirms Ohm's law:
the lower the voltage, the lower the amperage.
This is how this physical law works, which we face in everyday life.
A bonus, especially for you, a comic picture that no less colorfully explains Ohm's law.
This was a review article. In more detail about this law, we talk in the next article "", considering everything on other more complex examples.
If physics fails, English for children (http://www.anylang.ru/order-category/?slug=live_language) as a variant of alternative development.
Ohm's law for a section of a circuit is a law obtained experimentally (empirically) that establishes a relationship between the current strength in a section of a circuit with the voltage at the ends of this section and its resistance. The strict formulation of Ohm's law for a section of a circuit is written as follows: the current in a circuit is directly proportional to the voltage in its section and inversely proportional to the resistance of this section.
The Ohm's law formula for a chain section is written as follows:
I is the current in the conductor [A];
U - electrical voltage (potential difference) [V];
R - electrical resistance (or just resistance) of the conductor [Ohm].
Historically, the resistance R in Ohm's law for a section of a circuit is considered the main characteristic of a conductor, since it depends solely on the parameters of this conductor. It should be noted that Ohm's law in the above form is valid for metals and solutions (melts) of electrolytes and only for those circuits where there is no real current source or the current source is ideal. An ideal current source is one that does not have its own (internal) resistance. More information about Ohm's law as applied to a circuit with a current source can be found in our article. Let's agree to consider the positive direction from left to right (see the figure below). Then the voltage across the section is equal to the potential difference.
φ 1 - potential at point 1 (at the beginning of the section);
φ 2 - potential at point 2 (at the end of the section).
If the condition φ 1> φ 2 is satisfied, then the voltage U> 0. Consequently, the lines of tension in the conductor are directed from point 1 to point 2, and therefore the current flows in this direction. It is this direction of the current that will be considered positive I> O.
Consider the simplest example of determining resistance on a section of a circuit using Ohm's law. As a result of an experiment with an electrical circuit, an ammeter (a device that shows the current strength) shows, and a voltmeter. It is necessary to determine the resistance of the circuit section.
By the definition of Ohm's law for a section of a chain
When studying Ohm's Law for a section of a circuit in grade 8 school, teachers often ask students the following questions to reinforce the material they have learned:
Between what quantities does Ohm's law establish a relationship for a section of a chain?
Correct answer: between amperage [I], voltage [U] and resistance [R].
Why, apart from voltage, does the current strength depend?
Correct answer: From resistance
How does the current strength depend on the voltage of the conductor?
Correct answer: Directly proportional
How does current strength depend on resistance?
Correct answer: inversely proportional.
These questions are asked so that in grade 8 students can remember Ohm's law for sections of a circuit, the definition of which states that the current strength is directly proportional to the voltage at the ends of the conductor, if the resistance of the conductor does not change.
