Basic laws of DC circuits

RGR No. 1 Calculation of the DC electrical circuit

Direct current is an electric current that does not change in time either in strength or in direction. A direct current arises under the influence of a constant voltage and can only exist in a closed circuit; in all sections of an unbranched circuit, the direct current is the same. In real devices, the current strength, in accordance with Ohm’s law, changes with a change in load, therefore, in engineering, DC devices are considered to be such devices in which the current does not change its direction, but can change in magnitude. High power direct current sources are electric machine generators; direct current is also obtained by rectifying an alternating current.

Low power direct current sources are galvanic cells, thermoelements, photocells, which can be grouped into batteries (including solar panels), and low power electric machines. Secondary, pre-charged direct current sources are batteries. Direct current is used in various industries, e.g. in electrometallurgy, in traction motors in transport, in electric drives, when it is necessary to smoothly change the speed over a wide range, as well as in various communication, automation, signaling and telemechanics devices. It is promising to use high-voltage direct current in the transmission of electricity with virtually no losses through superconducting lines.

The calculation and analysis of electrical circuits is carried out using Ohm’s law, the first and second laws of Kirchhoff. Based on these laws, a relationship is established between the values of currents, voltages, EMF of the entire electrical circuit and its individual sections, and the parameters of the elements that make up this circuit.

Ohm’s law for a circuit section

The relationship between current I, voltage UR and resistance R of section ab of the electrical circuit (Fig. 1.1) is expressed by Ohm’s law.

Rice. 1.1

or (1.1)

In this case – called the voltage or voltage drop across the resistor R, and – current in the resistor R.

When calculating electrical circuits, it is sometimes more convenient to use not the resistance R, but the reciprocal of the resistance, i.e. electrical conductivity:

.

In this case, Ohm’s law for the circuit section will be written as:

Ohm’s law for the whole circuit

This law determines the relationship between the EMF E of a power source with internal resistance (Fig. 1.1), current I of the electrical circuit and total equivalent resistance the whole chain:

(1.2)

A complex electrical circuit contains, as a rule, several branches, in which their power sources can be included and the mode of its operation cannot be described only by Ohm’s law. But this can be done on the basis of the first and second laws of Kirchhoff, which are a consequence of the law of conservation of energy.

Kirchhoff’s first law

At any node of the electrical circuit, the algebraic sum of the currents is zero

(1.3),

where m is the number of branches connected to the node.

When writing equations according to the first Kirchhoff law, the currents directed to the node are taken with a plus sign, and the currents directed from the node are taken with a minus sign.

Kirchhoff’s second law

In any closed circuit of an electrical circuit, the algebraic sum of the EMF is equal to the algebraic sum of the voltage drops in all its sections

(1.4)

where n is the number of EMF sources in the circuit;

m is the number of elements with resistance in the contour;

– voltage or voltage drop on the k-th element of the circuit.

If voltage sources are included in the electrical circuit, then Kirchhoff’s second law is formulated as follows: the algebraic sum of the voltages on all counter elements, including EMF sources, is zero.

(1.5)

When calculating electrical circuits, certain units of measurement are used. Electric current is measured in amperes (A), voltage in volts (V), resistance in ohms (Ohm), power in watts (W), electrical energy in watt-hours (Wh) and conductivity in siemens ( Cm)

In addition to the basic units, smaller and larger units of measurement are used: milliamp (1mA = 10–3A), kiloampere (1kA = 103A), millivolt (1mV = 10–3V), kilovolt (1kV = 103V), kiloohm (1kOhm = 103Ohm) , megaohm (1mOhm = 106Ohm), kilowatt (1kW = 103W), kilowatt-hour (1kW-hour = 103 watt-hour).

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