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Series resistors

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Electrical circuits use various types of connections. The main ones are serial, parallel and mixed wiring diagrams. In the first case, several resistances are used, connected in a single chain one after another. That is, the beginning of one resistor is connected to the end of the second, and the beginning of the second - to the end of the third and so on, to any number of resistances. The current strength in series connection will be the same at all points and in all areas. To determine and compare other parameters of the electric circuit, other types of compounds that have their own properties and characteristics should be considered.

Series and parallel connection of resistances

Any load has a resistance that prevents the free flow of electric current. Its path passes from the current source, through the conductors to the load. For the normal passage of current, the conductor must have good conductivity and easily give off electrons. This provision will come in handy further when considering what a serial connection is.

Most electrical circuits use copper conductors. Each circuit contains energy receivers - loads with different resistances. The connection parameters are best viewed with an external current source circuit consisting of three resistors R1, R2, R3. Serial connection involves the sequential inclusion of these elements in a closed circuit. That is, the beginning of R1 is connected to the end of R2, and the beginning of R2 is connected to the end of R3 and so on. There can be any number of resistors in such a chain. These symbols use serial and parallel connections in the calculations.

The current strength in all sections will be the same: I = I1 = I2 = I3, and the total circuit resistance will be the sum of the resistances of all loads: R = R1 + R2 + R3. It remains only to determine what the voltage will be with a series connection. In accordance with Ohm's law, voltage is the strength of current and resistance: U = IR. It follows that the voltage at the current source will be equal to the sum of the voltages at each load, since the current is the same everywhere: U = U1 + U2 + U3.

With a constant voltage value, the current during a series connection will depend on the resistance of the circuit. Therefore, when the resistance changes at least on one of the loads, the resistance changes in the entire circuit. In addition, the current and voltage at each load will change. The main disadvantage of a serial connection is the termination of all elements of the circuit, in the event of failure of even one of them.

Completely different characteristics of current, voltage and resistance are obtained using a parallel connection. In this case, the beginnings and ends of the loads are connected at two common points. A kind of branching of the current occurs, which leads to a decrease in the total resistance and an increase in the total conductivity of the electric circuit.

In order to display these properties, Ohm's law will again be needed. In this case, the current strength in parallel connection and its formula will look like this: I = U / R. Thus, when the nth number of identical resistors is connected in parallel, the total resistance of the circuit will be n times less than any of them: Rtotal = R / n. This indicates an inverse proportional distribution of currents in the loads with respect to the resistances of these loads. That is, with an increase in parallel-connected resistances, the current strength in them will be proportionally reduced. In the form of formulas, all characteristics are displayed as follows: current strength - I = I1 + I2 + I3, voltage - U = U1 = U2 = U3, resistance - 1 / R = 1 / R1 + 1 / R2 + 1 / R3.

With a constant value of the voltage between the elements, the currents in these resistors are not dependent on each other. If one or more resistors are disconnected from the circuit, this will not affect the operation of other devices that remain on. This factor is the main advantage of parallel connection of electrical appliances.

In circuits, usually only serial connection and parallel resistance connection are not used, they are used in a combined form, known as mixed connection. To calculate the characteristics of such chains, the formulas of both versions are used. All calculations are divided into several stages, when the parameters of individual sections are first determined, after which they are added up and the overall result is obtained.

Laws of series and parallel connection of conductors

The main law used in the calculations of various types of compounds is Ohm's law. Its main position is the presence on the site of the circuit current strength, directly proportional to the voltage and inversely proportional to the resistance in this area. In the form of a formula, this law looks like this: I = U / R. It serves as the basis for the calculation of electrical circuits connected in series or in parallel. The order of calculations and the dependence of all parameters on Ohm's law are clearly shown in the figure. The formula for the serial connection is also derived from this.

More complex calculations involving other quantities require the application of the Kirchhoff rule. Its main position is that several series-connected current sources will have an electromotive force (EMF), which makes up the algebraic sum of the EMF of each of them. The total resistance of these batteries will consist of the sum of the resistances of each battery. If the nth number of sources with equal EMF and internal resistances is connected in parallel, then the total amount of EMF will be equal to the EMF at any of the sources. The value of internal resistance will be rv = r / n. These provisions are relevant not only for current sources, but also for conductors, including the parallel connection formulas of conductors.

In the case when the emf of the sources will have different meanings, additional Kirchhoff rules are applied to calculate the current strength in different parts of the circuit.

Series resistors

In the figure below, resistors R1, R2, and R3 are connected to each other in series between points A and B with a common current I, which flows through them.

The equivalent resistance of several series-connected resistors can be determined by the following formula:

That is, in our case, the total resistance of the circuit will be equal to:

R = R1 + R2 + R3 = 1 kOhm + 2 kOhm + 6 kOhm = 9 kOhm

Thus, we can replace these three resistors with just one “equivalent” resistor, which will have a value of 9 kOhm.

Where four, five or more resistors are connected together in a series circuit, the total or equivalent resistance of the entire circuit will also be equal to the sum of the resistances of the individual resistors.

It should be noted that the total resistance of any two or more resistors connected in series will always be greater than the largest resistance of the resistor included in this circuit. In the above example, R = 9 kOhm, while the largest value of the resistor is only 6 kOhm (R3).

The voltage on each of the resistors connected in series is subject to a different rule than the flowing current. As you know, from the above diagram, that the total supply voltage across the resistors is equal to the sum of the potential difference on each of them:

Using Ohm's law, the voltage across individual resistors can be calculated as follows:

As a result, the sum of the potential differences on the resistors is equal to the total potential difference of the entire circuit, in our example it is 9V.

In particular, a series of resistors connected in series can be considered as a voltage divider:

Using Ohm's law, it is necessary to calculate the equivalent resistance of a series of series-connected resistors (R1. R2, R3), as well as the voltage drop and power for each resistor:

All data can be obtained using Ohm's law and for a better understanding are presented in the form of the following table:

It is necessary to calculate the voltage drop at the terminals "A" and "B":

a) without a connected resistor R3

b) with connected resistor R3

As you can see, the output voltage U without a load resistor R3 is 6 volts, but the same output voltage when connecting R3 becomes only 4 V. Thus, the load connected to the voltage divider provokes an additional voltage drop. This effect of voltage reduction can be compensated by using a potentiometer installed instead of a constant resistor, with which you can adjust the voltage at the load.

Summarize

When two or more resistors are connected together (the output of one is connected to the output of the other resistor) - this is a series connection of resistors. The current flowing through the resistors has the same value, but the voltage drop across them is not the same. It is determined by the resistance of each resistor, which is calculated according to Ohm's law (U = I * R).

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