How to calculate amperage: physical formulas using power and voltage

When choosing any electrical equipment, one of the important parameters to which attention is drawn is the power of the product. This parameter is inextricably linked to current and voltage. To calculate the current, voltage or power in an electrical circuit, simple formulas are used. But in order to meaningfully carry out such calculations, it is desirable to understand the physical nature of the occurrence of these quantities.

Physical concept of quantities

Any electrical circuit is characterized by a number of parameters. The most important of these are amperage, voltage, wattage, and resistance. These characteristics are related and dependent on each other. The phenomenon that unites them is called electricity.

This concept was introduced back in 1600 by the English physicist William Gilbert, who studies magnetic and electrical phenomena. Studying magnetism in nature, the scientist found that some bodies, when rubbed, begin to have a force of attraction in relation to other objects, in particular, to amber. Therefore, he called the open phenomenon ēlectricus, which translated from Latin means "amber".

Continuing his research, the German physicist Otto von Guericke in 1663 invented an electric machine, which was a metal rod with a sulfur ball on it. As a result, he found out that materials can not only attract substances, but also repel. But only eighty years later, the American Benjamin Franklin created the theory of electricity, introducing terms such as negative and positive charges.

Electricity received further development after the experiments of Charles Coulomb and his discovery of the law of interaction of charges. It consisted in the following: the force of influence of two point charges on each other in a vacuum is directly proportional to their product and inversely proportional to the distance between them in a square. After that, thanks to the experiments of such scientists as Joule, Lenz, Ohm, Ampere, Faraday, Maxwell, the concepts of current, voltage and electromagnetism were introduced.

So, in 1897, the Englishman Joseph Thomson established that the charge carriers are electrons. Earlier, in 1880, an electrical engineer from Russia Dmitry Lachinov formulated the necessary conditions for the transmission of electricity over a distance.

Following these discoveries, fundamental definitions of electricity were developed. Today, it refers to the properties of materials to form an electric field around them, which affects other charged particles located nearby. Charges are conventionally divided into positive and negative ones. When they move, a magnetic field arises, while charges of the same sign are attracted, and different charges are repelled.

Current strength

Current is the ordered movement of charge carriers under the influence of an electric field. Electrons act as positively charged particles, and holes as negative ones. Mathematically, this phenomenon is described using the formula I = Q * T, where I is the conduction current (A), Q is the particle charge (C), T is the time ©.

That is, the electric current is the amount of charges that have passed through the cross section of the substance. But this formulation is correct only for a constant current, while for a time-varying current it will look like I (T) = dQ / dT.

The density of movement of charge carriers in a material, that is, the amount of electricity passing in a conventionally accepted time, is called the current strength. According to the International System (SI), its unit of measurement is ampere. One ampere is equal to the movement of an electric charge equal to one coulomb through the cross section in one second.

Charge carriers can move both orderly and chaotically. When they move, an electric field appears, denoted by the Latin letter E. The value determined by the ratio of the current to the cross section of the conductor is called the current density. A / mm is taken as the unit of its measurement.².

By its type, the current is distinguished into the following types:

1. Carryover. It is characterized by the movement of charges carried out in free space. This type is typical for gas-discharge devices.
2. Offsets. It arises in dielectrics and is determined by the ordered movement of bound charged particles.
3. Full. It is determined by the sum of the current: conductance, transfer and displacement.
4. Constant. This is a species that can change the value, but does not change the direction of movement, that is, its sign.
5. Variable. This type of current can vary both in magnitude and in direction (sign).

The variable view is divided in shape and can be sinusoidal and non-sinusoidal. To calculate the sinusoidal current, use the formula Is = Ia * sin ωt, where Ia is the maximum value of the current (A), ω is the angular velocity equal to 2πf (Hz).

Physical bodies in which the flow of current is possible are called conductors, and in those where there are obstacles to its passage - dielectrics. An intermediate state between them is occupied by semiconductors.

Potential difference

It is customary to call voltage a physical quantity that characterizes an electric field. It shows what kind of work the field will need to do in order to move a unit charge from one point to another. It is assumed that this transfer does not affect the distribution of charges in the field source. According to the International System of Units, voltage is measured in volts.

The transfer work consists of two quantities - electrical and third-party. If external forces do not act, then the voltage on the circuit section is equal to the potential difference and is calculated by the formula U = φ1-φ2. In this case, the potential is determined by the ratio of the electric field strength to the charge. To calculate it, use the formula φ = W / q.

In other words, this is the characteristic of the field at a certain point, independent of the magnitude of the charge in it. That is, the voltage is generally determined by the work of the electrostatic field that occurs when the charge moves along its lines of force. Mathematically, it can be calculated by the formula U = A / q, where A is the work being done to move (J), q is the charge energy (C).

The following terms are used for voltage when applied to AC mains:

1. Instant. This is the value of a physical quantity measured at a specific point in time: U = U (t). For a sinusoidal signal, the instantaneous voltage is found using the expression U (t) = Ua sin (ὤt + φ).
2. Amplitude. It is characterized by the largest instantaneous value without taking into account the sign: Ua = max (U (t)).
3. The average. It is determined for the full period of the signal by the formula Us = 1 / T ʃ U (t) * dt. For a sinusoidal waveform, this value is zero.

When calculating voltage, the concept of electric potential is rarely used. This is due to the fact that it is conventionally taken as one of the points of potential to take the earth.

This value is taken equal to zero, and all other potentials are considered relative to it. When we say that the voltage at a certain point is 300 volts, we mean the potential difference between this point and ground, equal to this value.

Electric power

Electrical power characterizes the rate at which electrical energy is transmitted or converted. Its unit of measurement is watt. In order to calculate the power in a certain section of the circuit, it is necessary to multiply the value of the voltage and current in this section. Based on the definition of electric voltage, we can say that the charge, when moving, performs work, numerically equal to it in the section of the circuit. If we multiply the work by the number of charges, then we can find the total value of the work that the charges have done in this area.

Based on the physical definition that power is work per unit of time, the expression is obtained P = A / Δt, where A is the work done by the charge when moving from the initial point to the final one (J), Δt is the time spent on the complete movement of the charge ©.

For all charges in the circuit, the power can be found using the formula P = (U / Δt) * Q, where Q is the total number of charges.

Since the current is a charge flowing per unit of time (I = Q / Δt), it turns out that the power is equal to the product of current and voltage, that is P = U * I (Tue).

In a circuit with a constant current, its strength and voltage always have a constant value at a certain point, therefore, for any moment in time, the power can be calculated by the formula P = I * U = I2 * R = U2 / R, where R is the resistance to the passage of current in the electrical circuit (Ohm). If there is a source of electromotive force in this network, then the power is found as P = I * E + I2 * r, where E is the electromotive force or EMF (V), r is the internal resistance of the EMF source (Ohm).

For a circuit in which its parameters change in a certain cycle, the power at a certain point is integrated over time. In this case, there are the following types of power:

1. Active. To find it, a calculation is used that takes into account the phase angle φ. It is found according to the formula P = U * I * cos φ.
2. Reactive. It is characterized by loads created by electrical devices in the form of fluctuations in the energy of an electromagnetic field. Its calculation is carried out according to the formula P = U * I * sin φ.
3. Full. It is determined by the product of the effective values ​​of current and voltage, and is associated with other types of power by the expression S = √ (P ² + Q ²).

Ohm's law for a chain

When calculating power for voltage and current in practice, Ohm's law is often used. It establishes a relationship between current, resistance and voltage. This law was discovered through a series of experiments conducted by Simon Ohm and formulated by him in 1826. He found that the amount of current in a section of the circuit is directly proportional to the potential difference and inversely proportional to the resistance of this section.

Ohm's law can be written as follows: I = U / R, where I is the value of the current strength (A), U is the potential difference (V), R is the resistance of the circuit to the passage of current (Ohm).

For a complete chain, this formula can be written as follows: I = E / (R + r0), where E is the EMF of the power source (V), r0 is the internal resistance of the voltage source (Ohm).

Thus, for the section of the chain, the expression P = U2 / R = I2R, and for a complete chain - P = (E / (R + R0))²* R. It is these two formulas that are most often used to calculate electrical networks or the power of the required equipment.

Different components of the electrical network at a certain point in time consume different amounts of current. Therefore, it is very important to correctly calculate how much energy is supplied at one time or another. to a certain place in the chain in order to prevent overloads on the line and the occurrence of emergency situations.

This is what circuit designers do, simplifying them to the point where you can calculate the required power using Ohm's law.

Practical calculation

For example, suppose you need to find out for what current you need to purchase a circuit breaker installed on a section of the circuit. At the same time, it is known that the refrigerator with maximum power consumption of one kilowatt, a boiler (two kilowatts) and a chandelier consuming 90 watt. The installation site uses a single-phase network designed for an operating voltage of 220 volts.

At the first stage of the calculation, you will need to summarize the entire power of the electrical appliances connected to the line. So, P total. = 1000 + 2000 + 90 +220 = 3310 W. Using the formula P = I * U, the required current value is found: I = P / U = 3310/220 = 15.04 A.

Of the standard range of switches, the closest value is a 16 A circuit breaker. Since it is necessary to buy a protection device with a small margin, a switch designed for 20 amperes is suitable for this example.

Thanks to such calculations, you can calculate any parameter of the electrical circuit, but this is taking into account a sufficient amount of input data.