Базовые элементы электрических цепей

Algorithm for calculating electrical circuits using

Algorithm for calculating electrical circuits using

nodal potential method

• Equate the potential of one of the nodes 0;
• Compose the equations by the method of nodal potentials.

On the right side of the equations, the sign is determined as follows: if the EMF is directed to the node, then it has a (+) sign, if from the node - (-);

3. We calculate the equations, determine the potentials.

4. Determine the currents according to the formulas given earlier.

Power balance

When solving electrical problems, it is often necessary to check the correctness of the found values. For this, in the science of TEC, there is a so-called power balance.

The power balance is an expression of the law of conservation of energy in an electrical circuit. The definition of the power balance is as follows: the sum of the powers consumed by the receivers is equal to the sum of the powers given by the sources. That is, if the EMF source in the circuit gives off 100 W, then the receivers in this circuit consume exactly the same power.

or

Let's check this relationship with an example

First, let's turn aside (close) the circuit and find the equivalent resistance. R2 and R3 are connected in parallel.

We will find, according to Ohm's law, the source current and the voltage across R23, taking into account that r1 and R23 are connected in series, therefore, the current strength is the same.

Find currents I2 и I3

Now let's check the correctness using the power balance.

The slight difference in values ​​is due to rounding off during the calculation.

Energy balance equation

For any electrical circuit, the power consumed by the resistors in this circuit must equal the power of the energy sources. The energy balance equation (power balance) in general form is written as follows:

On the left side of the equation, the power of the energy sources is taken into account. The power of the EMF sources is taken into account with a positive (negative) sign if the current flowing through the EMF source coincides (opposite) with the direction of the EMF. To determine the sign of the power of the current source, it is necessary to determine the voltage at the source. If the source current flows from a point of lower potential and flows to a point of higher potential, the power of the source will be positive (the source generates energy).

If the source current flows out from a point of higher potential than the potential of the point where the current flows, the power of the source will be negative, and its mode of operation corresponds to the energy consumption.

On the right side of the energy balance equation, the arithmetic sum of the powers consumed by the circuit resistors and determined according to the Joule-Lenz law is written. In terms of their physical meaning, these powers can only be positive.

1. Method of loop (contour) currents. 2. Method of nodal voltages. 3. Method of nodal potentials. 4. Power balance.

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