Ohm's law for a section of a chain and a complete chain: formulas and explanation

For an electrician and electronics engineer, one of the basic laws is Ohm's Law. Every day the work sets new tasks for the specialist, and often it is necessary to find a replacement for a burnt out resistor or a group of elements. An electrician often has to change cables, in order to choose the right one, you need to "estimate" the current in the load, so you have to use the simplest physical laws and ratios in everyday life. The importance of Ohm's Law in electrical engineering is colossal, by the way, most of the diploma works of electrical engineering specialties are calculated by 70-90% according to one formula.

Historical reference

Ohm's Law was discovered in 1826 by the German scientist Georg Ohm. He empirically defined and described the law of the relationship between current strength, voltage and type of conductor. Later it turned out that the third component is nothing more than resistance. Subsequently, this law was named after the discoverer, but the law was not limited to the matter, his surname and the physical quantity was named, as a tribute to his work.

The value in which resistance is measured is named after Georg Ohm. For example, resistors have two main characteristics: power in watts and resistance - a unit of measurement in ohms, kilo-ohms, mega-ohms, etc.

Ohm's law for a section of a chain

To describe an electrical circuit that does not contain EMF, you can use Ohm's law for a section of the circuit. This is the simplest form of recording. It looks like this:

I = U / R

Where I is current, measured in Amperes, U is voltage in volts, R is resistance in ohms.

This formula tells us that current is directly proportional to voltage and inversely proportional to resistance - this is the exact formulation of Ohm's Law. The physical meaning of this formula is to describe the dependence of the current through a section of the circuit at a known resistance and voltage.

Attention! This formula is valid for direct current, for alternating current it has slight differences, we will return to this later.

In addition to the ratio of electrical quantities, this form tells us that the graph of the dependence of the current on the voltage in the resistance is linear and the equation of the function is fulfilled:

f (x) = ky or f (u) = IR or f (u) = (1 / R) * I

Ohm's law for a section of a circuit is used to calculate the resistance of a resistor in a section of a circuit or to determine the current through it at a known voltage and resistance. For example, we have a 6-ohm resistor R with a voltage of 12 V applied to its terminals. It is necessary to find out how much current will flow through it. Let's calculate:

I = 12V / 6 Ohm = 2A

An ideal conductor has no resistance, however, due to the structure of the molecules of the substance of which it is composed, any conducting body has resistance. For example, this was the reason for the transition from aluminum to copper wires in household power grids. The resistivity of copper (ohms per meter length) is less than that of aluminum. Accordingly, copper wires heat up less, withstand high currents, which means you can use a wire of a smaller cross-section.

Another example - the spirals of heating devices and resistors have a high specific resistance, because are made of various high-resistance metals, such as nichrome, kantal, etc. When charge carriers move through a conductor, they collide with particles in the crystal lattice, as a result of which energy is released in the form of heat and the conductor heats up. The more current - the more collisions - the more heating.

To reduce heating, the conductor must be either shortened or increased in thickness (cross-sectional area). This information can be written in the form of a formula:

R_{the wire}= ρ (L / S)

Where ρ is the resistivity in Ohm * mm²/ m, L - length in m, S - cross-sectional area.

Ohm's law for parallel and series circuit

Depending on the type of connection, there is a different pattern of current flow and voltage distribution. For a section of a chain of series connection of elements, voltage, current and resistance are found by the formula:

I = I1 = I2

U = U1 + U2

R = R1 + R2

This means that the same current flows in a circuit of an arbitrary number of series-connected elements. In this case, the voltage applied to all elements (the sum of the voltage drops) is equal to the output voltage of the power supply. Each element individually has its own voltage value and depends on the current strength and specific resistance:

U_e-mail= I * R_element

The resistance of the circuit section for parallel-connected elements is calculated by the formula:

I = I1 + I2

U = U1 = U2

1 / R = 1 / R1 + 1 / R2

For a mixed connection, you need to bring the chain to an equivalent form. For example, if one resistor is connected to two parallel-connected resistors, then first calculate the resistance of the parallel-connected ones. You will get the total resistance of the two resistors and you just have to add it to the third, which is connected in series with them.

Ohm's law for a complete circuit

A complete circuit assumes a power source. An ideal power source is a device that has one characteristic:

• voltage, if it is an EMF source;
• current strength, if it is a current source;

Such a power supply is capable of delivering any power with constant output parameters. In a real power supply, there are also parameters such as power and internal resistance. In fact, the internal resistance is an imaginary resistor installed in series with the EMF source.

The Ohm's Law formula for a complete circuit looks similar, but the internal resistance of the PI is added. For a complete chain, it is written by the formula:

I = ε / (R + r)

Where ε is the EMF in Volts, R is the load resistance, r is the internal resistance of the power source.

In practice, the internal resistance is a fraction of Ohm, but for galvanic sources, it increases significantly. You observed this when two batteries (new and dead) have the same voltage, but one gives out the required current and works properly, and the second does not work, because sags at the slightest load.

Ohm's law in differential and integral form

For a homogeneous section of the circuit, the above formulas are valid; for an inhomogeneous conductor, it is necessary split into the shortest possible segments so that changes in its size are minimized within this segment. This is called Ohm's Law in differential form.

In other words: the current density is directly proportional to the strength and conductivity for an infinitely small section of the conductor.

In integral form:

Ohm's law for alternating current

When calculating AC circuits, instead of the concept of resistance, the concept of "impedance" is introduced. The impedance is denoted by the letter Z, it includes the resistance of the load R_a and reactance X (or R_r). This is due to the shape of the sinusoidal current (and currents of any other forms) and the parameters of the inductive elements, as well as the laws of commutation:

1. The current in a circuit with inductance cannot change instantly.
2. The voltage in a circuit with a capacitance cannot change instantly.

Thus, the current begins to lag behind or ahead of the voltage, and the apparent power is divided into active and reactive.

U = I * Z

X_L and X_C Are the reactive components of the load.

In this regard, the cosF value is introduced:

Here - Q is the reactive power due to alternating current and inductive-capacitive components, P - active power (allocated to active components), S - apparent power, cosФ - coefficient power.

You may have noticed that the formula and its presentation overlaps with the Pythagorean theorem. This is indeed the case, and the angle Ф depends on how large the reactive component of the load is - the more it is, the more it is. In practice, this leads to the fact that the current actually flowing in the network is greater than that which is taken into account by the household meter, while enterprises pay for the full capacity.

In this case, resistance is presented in a complex form:

Here j is the imaginary unit, which is typical for the complex form of equations. Less commonly denoted as i, but in electrical engineering, the rms value of an alternating current is also denoted, therefore, in order not to get confused, it is better to use j.

The imaginary unit is √-1. It is logical that there is no such number when squaring, which can get a negative result "-1".

How to remember Ohm's law

To memorize Ohm's Law, you can memorize the formulation in simple words like:

The higher the voltage, the higher the current, the higher the resistance, the lower the current.

Or use mnemonic pictures and rules. The first is a pyramid-like representation of Ohm's law - brief and understandable.

A mnemonic rule is a simplified form of a concept for its simple and easy understanding and study. It can be either verbal or graphical. To find the right formula correctly, close the required value with your finger and get the answer in the form of a product or quotient. This is how it works:

The second is a caricature show. It is shown here: the more Ohm tries, the more difficult the Ampere passes, and the more Volts, the easier the Ampere passes.

Finally, we recommend watching a useful video, which explains Ohm's Law and its application in simple words:

Ohm's law is one of the fundamental in electrical engineering, without his knowledge, most of the calculations are impossible. And in everyday work, you often have to translate amperes to kilowatts or determine the current by resistance. It is not at all necessary to understand its conclusion and the origin of all quantities - but the final formulas are obligatory for mastering. In conclusion, I would like to note that there is an old comic proverb from electricians: "If you don't know Om, stay at home." And if in every joke there is a grain of truth, then here this grain of truth is 100%. Study the theoretical foundations if you want to become a professional in practice, and other articles from our site will help you with this.