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# What Is a Mathematical Law of Resistors in Series

The total resistance of this combination lies between the pure series and the pure parallel values (or , ). As discussed in Lesson 1, the electrochemical cell of a circuit supplies energy to the load to move it through the cell and create a difference in electrical potential between the two ends of the external circuit. A 1.5 volt cell produces a 1.5 volt electrical potential difference through the external circuit. This means that the electric potential at the positive terminal is 1.5 volts higher than that of the negative pole. As the load travels through the external circuit, it loses 1.5 volts of electric potential. This loss of electrical potential is called voltage drop. It occurs when the electrical energy of the load is converted into other forms of energy (thermal, light, mechanical, etc.) in resistors or loads. If a circuit powered by a 1.5 volt cell is equipped with more than one resistor, the cumulative loss of electrical potential is 1.5 volts. There is a voltage drop for each resistor, but the sum of these voltage drops is 1.5 volts – the same voltage as the nominal voltage of the power supply. This concept can be expressed mathematically by the following equation: This equation is called the Kirchhoff connection rule and will be discussed in detail in the next section. Figure 6.2.4 shows the junction rule.

There are two loops in this circuit that lead to the equations and Note that the voltage at the resistances is the same in parallel () and that the current is additive: consider the same potential difference applied to the same three resistors connected in series. Would the equivalent resistance of the serial connection be greater, less than or equal to the three resistors in parallel? Would the current of the series connection be greater, less than or equal to the current supplied by the same voltage applied to the parallel circuit? How would the power delivered by the series resistor compare to the power delivered by the parallel resistors? As mentioned in the previous section of lesson 4, two or more electrical devices in a circuit can be connected in series or through parallel connections. When all devices are connected in series, the circuit is called a serial chain. In a serial connection, each device is connected in such a way that there is only one way by which the load can pass through the external circuit. Each load circulating in the loop of the external circuit passes through each resistor one by one. In this chapter, we have presented the equivalent resistance of resistors connected in series and resistors connected in parallel. You may recall that in Capacitance, we introduced the equivalent capacitance of capacitors connected in series and in parallel. Circuits often contain both capacitors and resistors. Table 6.2.1 summarizes the equations used for equivalent strength and equivalent capacitance for serial and parallel connections.

Then, when we know that the current is divided equally by all the components of a serial connection (another « rule » of serial connections), we can fill the currents for each resistor from the current number that has just been calculated: Let`s briefly summarize the main characteristics of series resistors: Understand how to derive formulas from a series of resistors in series or in parallel, may be necessary in some cases. And it also helps to understand the general theory of circuits. If we generalize to any number of resistors, the equivalent resistance of a parallel connection is related to the individual resistances by b. The current passing through the circuit is the same for each resistor of a series connection and corresponds to the applied voltage divided by the equivalent resistance: d. Three resistors with resistance values of 2-Ω, 4-Ω and 6-Ω are connected in series. These would provide a resistance equivalent to a resistance of 12 Ω. Some miniature Christmas light chains are shortened when a light bulb burns. The device causing the short circuit is called a shunt, which allows current to flow around the open circuit. A « short circuit » is like placing a piece of wire on the component. The bulbs are usually grouped in a row of nine onions.

If too many blisters burn, the shunts eventually open. What for? Second, Kirchoff`s laws state that the sum of the tensions around a circuit is zero. Thus, the sum of the voltage drops through the resistors is equal to the voltage provided by the source in the circuit represented. Note that the total power delivered by the resistors is equal to the power provided by the source. Three resistors, and are connected in parallel. The parallel connection is connected to a voltage source. a) What is an equivalent resistance? b) Find the current supplied by the source to the parallel circuit. (c) Calculate the currents in each resistor and show that they add up to match the current output of the source.

(d) Calculate the power dissipation of each resistor. e) Find the output power of the source and show that it corresponds to the total power dissipated by the resistors. At a total VAB voltage of (1V + 2V + 6V) = 9V, which corresponds to the value of the supply voltage. Thus, the sum of the potential differences between the resistors is equal to the total potential difference on the combination and 9V. The equation for calculating the total voltage in a serial connection, which adds up the sum of all the individual voltages, is as follows: Since we know that the current through all the components of a serial connection is the same (and we have just determined the current through the battery), we can go back to our original diagram and note the current through each component: The total resistance of any serial connection is equal to the sum of the individual Resistors. The number of 9 volts is a total size for the entire circuit, while the numbers of 3k, 10k and 5k are Ω individual sizes for individual resistors. If we were to insert a total voltage number into an Ohm`s law equation with a number for the individual resistance, the result would not refer exactly to a quantity in the real circuit. Note that the resistors and are in series. They can be combined into a single equivalent resistor. One way to follow the process is to include resistance as an index. Here, the equivalent resistance of and is called series resistors if it is due to their single-line chain arrangement.

This causes a common flow to pass through them. Here, the individual resistors can be connected in series. A parallel circuit or combinations of series and parallel connections can be made to create a more complex resistor network. In the compound, the equivalent resistance is the mathematical combination of the individual interconnected resistances. The resistors are connected in series each time the current flows sequentially through the resistors. Consider Figure 6.2.2, which shows three resistors in series with an applied voltage. Since there is only one path through which charges can flow, the current is the same through any resistance. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances. The resistors and are in series, so the currents and are equal Let`s take a look at some examples of series circuits that demonstrate these principles. Since they are in series, the current is equal to the through current. There, the current will be throughout everyone. The power dissipated by the resistors is equal to the sum of the power dissipated by each resistor: On this page, we describe the three principles you need to understand regarding series connections: As mentioned earlier, since the resistors are connected in series, the same current flows through each resistor in the chain.

The total resistance RT of the circuit must be equal to the sum of all the different resistances. Taking into account the individual values of the resistances, the total equivalent resistance, REQ can be specified as follows: 2. When the number of resistors in a series connection increases, the total resistance ____ (increases, decreases, remains the same) and the current in the circuit __ (increases, decreases, remains the same). In addition, with the current flowing through the circuit, the current flowing through the resistors is common. Indeed, the current passing through one resistor must also flow through the others, because it circulates only by one path. Then we can say that the amount of current flowing in series through a series of resistors is the same at all points of a series of resistance networks. In a printed circuit board, the applications of series resistors are so extensive that they can be used to generate different voltages on themselves. These types of resistor networks are also useful for the manufacture of voltage divider networks. When one of the resistors in the voltage splitter circuit is replaced with a sensor such as a thermistor, a light-dependent resistor (LDR), or a switch, a detected analog quantity is converted into a suitable electrical signal that can be measured. The resistance tutorial includes: What is resistance Ohm`s Law Resistive and non-ohmic conductors Incandescent lamp resistance Table of resistance for common materials Resistance temperature coefficient Resistance resistance voltage coefficient, VCR Electrical conductivity Series and parallel resistors Table of parallel resistances The equivalent resistance of a combination of resistors depends both on their values individual and how they are connected. The simplest combinations of resistors are series circuits and parallel circuits (Figure 6.2.1).

In a series connection, the output current of the first resistor flows into the input of the second resistor; Therefore, the current is the same in any resistance.

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