9 junio, 2024

Mixed electrical circuit: what it is, characteristics, parts, symbols, examples

We explain what a mixed circuit is, its characteristics, parts, symbols and we give several examples.

What is a mixed circuit?

He mixed electrical circuit It is the one that contains elements connected both in series and in parallel, so that, when closing the circuit, different voltages and currents are established in each one of them.

Circuits are designed for a wide variety of purposes and their elements fall into two categories: active and passive.

The active elements of the circuit are the generators or sources of voltage or current, direct or alternating. On the other hand, the passive elements are the resistors, the condensers or capacitors and the coils. Both of them admit serial and parallel connections, as well as combinations of these.

The figure above shows, by way of example, a mixed-type association of electrical resistors with a battery and a switch. Resistors R1, R2, and R3 are connected in series, while resistors R4, R5, and R6 are connected in parallel.

Other possible connections, different from series-parallel associations, are delta (or delta) and star, often used in electrical machines powered by alternating current.

Characteristics of a mixed circuit

In general terms, in a mixed circuit the following can be observed:

The power of the circuit can be through a direct generator (battery) or alternating.
It is considered that the cables or wires that join the different elements do not offer resistance to the current.
Both voltage and current can be constant or variable in time. Capital letters are used to denote constant values, and lower case when they are variables.
In purely resistive mixed circuits, the current through resistors in series is the same, while in resistors in parallel it is generally different. To calculate the current and voltage through each resistance, we usually reduce the circuit to a single resistance, called the equivalent resistance, or Req .

series resistors

resistors in parallel

If the circuit consists of n capacitors, when they are associated in series the equivalent capacitance Ceq results:

series capacitors

capacitors in parallel

Coils or inductors follow the same association rules as resistors. Thus, when you want to reduce an association of coils in series to obtain the equivalent inductance Leq, the following formulas are used:

series inductors

inductors in parallel

Ohm’s law and Kirchoff’s laws are used to solve mixed circuits with resistors. For simple resistive circuits, Ohm’s law suffices, but for more complex networks Kirchoff’s laws need to be applied in combination with Ohm’s law, in addition to the relationship between voltage and current for capacitors and coils, if these elements are also present. present.

Relationship between voltage and current

Depending on the circuit element, there is a relationship between the voltage or voltage across the element with the intensity of the current that passes through it:

resistance R

Ohm’s law is used:

vR

Capacitor C

inductance L

Parts of a mixed circuit

In an electrical circuit the following parts are distinguished:

Knot

Junction point between two or more conductive wires that connect some active or passive element of the circuit.

Branch

Elements, whether active or passive, found between two consecutive nodes.

Mesh

Closed portion of the circuit covered without going through the same point twice. It may or may not have a voltage or current generator.

Kirchoff’s laws or rules

Kirchoff’s rules apply whether the currents and voltages are constant or time dependent. Although they are often called laws, they are actually rules for applying conservation principles to electrical circuits.

First rule

It establishes the principle of conservation of charge, by noting that the sum of the currents entering a node is equivalent to the sum of the currents leaving it:

∑ Iin = ∑ Iout

Second rule

On this occasion, the principle of conservation of energy is established, when it states that the algebraic sum of the voltages in a closed portion of the circuit (mesh) is zero.

∑ Vi = 0

symbols

To facilitate the analysis of circuits, the following symbols are used:

Examples of mixed circuits

Example 1

Draw the mixed circuit of the beginning figure in compact form, by using the symbols described above.

Answer

Example 2

In the circuit of example 1 we have the following values ​​for the resistors and the battery:

R1 = 50 ohms; R2 = 100 ohms; R3 = 75 Ω, R4 = 24 Ω, R5 = 48 Ω; R6 = 48 ohms; ε = 100V

For the circuit shown, the battery is considered ideal, that is, it has no internal resistance. Real batteries usually have a small internal resistance that is drawn in series with the cell and is treated the same as the other resistors in the circuit.

Calculate the following:

a) The equivalent resistance of the circuit.
b) The value of the current that leaves the battery.
c) The voltages and currents in each of the resistors.

Answer to

The first group of resistors: R1 = 50 Ω; R2 = 100 ohms; R3 = 75 Ω are connected in series, therefore the equivalent resistance is R123:

R123 = R1 + R2 + R3 = 50 Ω + 100 Ω + 75 Ω = 225 Ω

As for the group of resistors R4 = 24 Ω, R5 = 48 Ω; R6 = 48 Ω, they are connected in parallel and the corresponding formula must be applied:

The reciprocal or inverse of the previous result is the equivalent resistance for the group:

R456 = 12 ohms

The simplified circuit that is obtained is shown in the following graph, consisting of two resistors in series with the cell or battery. These two resistances are added to find the equivalent resistance of the original circuit Req:

Req= 225 Ω + 12 Ω = 237 Ω

answer b

The current coming out of the battery (by convention it is always drawn coming out of the positive pole) is calculated with the simplified circuit, which consists of the equivalent resistance Req in series with the battery, to which Ohm’s law is applied:

ε = I R

I = ε / R = 100 V / 237 Ω = 0.422 A

answer c

The voltages and currents in each of the resistors are calculated using Ohm’s law. The first thing you notice is that the current leaving the battery goes all the way through resistors R1 , R2 , and R3 and instead divides as it goes through R4 , R5 , and R6.

The voltages V1, V2 and V3 are:

V1 = 0.422 A × 50 Ω = 21.1 V
V2 = 0.422 A × 100 Ω = 42.2 V
V3 = 0.422 A × 75 Ω = 31.7 V

On the other hand, the voltages V4, V5 and V6 have the same value, since the resistances are in parallel:

V4 = V5 = V6 = 0.422 A × 12 Ω = 5.06 V

And the respective currents are:

I4 = 5.06 V / 24 Ω = 0.211 A

I5 = I6 =5.06 V / 48 Ω = 0.105 A

Note that adding I4, I5 and I6 again gives the total current coming out of the battery.

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