Physics
Series and Parallel Circuits
Series and parallel circuits are two fundamental arrangements of electrical components. In a series circuit, the current has only one path to flow through all the components, while in a parallel circuit, the current has multiple paths to flow through different branches. Series circuits have the same current passing through each component, while parallel circuits have the same voltage across each component.
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10 Key excerpts on "Series and Parallel Circuits"
eBook - PDF- Stephen Herman(Author)
- 2019(Publication Date)
- Cengage Learning EMEA(Publisher)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 124 SECTION 2 Basic Electric Circuits OBJECTIVES After studying this unit, you should be able to ● discuss the properties of series circuits. ● list three rules for solving electrical values of series circuits. ● calculate values of voltage, current, resistance, and power for series circuits. ● calculate the values of voltage drop in a series circuit using the voltage divider formula. Preview E lectric circuits can be divided into three major types: series, parallel, and combination. Combination circuits are circuits that contain both series and parallel paths. The first type discussed is the series circuit. 6–1 Series Circuits A series circuit is a circuit that has only one path for current flow (Figure 6–1) . Because there is only one path for current flow, the current is the same at any point in the circuit. Imagine that an electron leaves the negative terminal of the battery. This electron must flow through each resistor before it can complete the circuit to the positive battery terminal. One of the best examples of a series-connected device is a fuse or circuit breaker (Figure 6–2) . Because fuses and circuit breakers are connected in series with the rest of the circuit, all the circuit current must flow through them. If the current becomes excessive, the fuse or circuit breaker will open and disconnect the rest of the circuit from the power source. 6–2 Voltage Drops in a Series Circuit Voltage is the force that pushes the electrons through a resistance.
- Frank R. Spellman(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
A dangerously large current will flow when a short circuit occurs. A short circuit is usually caused by an accidental connection between two points in a circuit that offers very little resistance and passes an abnormal amount of current. A short circuit often occurs because of improper wiring or broken insulation. 10.17 PARALLEL DC CIRCUITS The principles we applied to solving simple series circuit cal-culations for determining the reactions of such quantities as voltage, current, and resistance can be used in parallel and series–parallel circuits. 10.17.1 P ARALLEL C IRCUIT C HARACTERISTICS A parallel circuit is defined as one having two or more components connected across the same voltage source (see Figure 10.44). Recall that a series circuit has only one path for current flow. As additional loads (resistors, etc.) are added to the circuit, the total resistance increases and the total current decreases. This is not the case in a parallel circuit. In a parallel circuit, each load (or branch) is con-nected directly across the voltage source. In Figure 10.44, commencing at the voltage source ( E b ) and tracing coun-terclockwise around the circuit, two complete and separate paths can be identified in which current can flow. One path is traced from the source through resistance R 1 and back to the source, the other from the source through resistance R 2 and back to the source. 10.17.2 V OLTAGE IN P ARALLEL C IRCUITS Recall that in a series circuit the source voltage divides pro-portionately across each resistor in the circuit. In a parallel circuit (see Figure 10.44), the same voltage is present across all of the resistors of a parallel group. This voltage is equal E 1 = 20 volts R 1 E 2 = 60 volts C + 60 volts B + 20 volts A 0 volts 80 volts R 2 FIGURE 10.41 Use of ground symbols. E b R 2 + – R 1 I Conducting chassis I FIGURE 10.42 Ground used as a conductor. R 1 R 2 E b Switch Fuse (open) + – FIGURE 10.43 Open circuit with blown fuse.
eBook - PDFElectricity and Electronics for Renewable Energy Technology
An Introduction
- Ahmad Hemami(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
At large scale, consider a city where each house has several devices (e.g., lights, radio, TV, kitchen appliances). Today, electricity in cities is pro-vided by more than one source. The power network, or grid, is fed at different points. So, we need to study the cases where there is more than one power source. New terms: Combined circuit, equivalent resistor, parallel circuit, series circuit, time constant, voltage divider 6 106 Electricity and Electronics for Renewable Energy Technology In this chapter we discuss how to deal with such circuits when con-nected to a DC source. In Chapter 8 we discuss these combinations in AC circuits. 6.2 Series Circuit When a number of components are put together in such a way that when connected to a source they form a single loop, we say these components are in series (with each other), and the circuit formed this way is called a series circuit . A series circuit is shown in Figure 6.1. In this circuit, there are three resistors (or resistive components) and two inductors in series and connected to 110 V. A switch is added for turning the power on and off. Note that it is not defined if the 110 V source is DC or AC (when no other information is included). In the case it was DC we could show the source by a symbol for battery, and in the case it was an AC source we could write 110 VAC (when an AC source is used, normally the frequency should also be given). Because there is only one loop, there is only one current for all the components. This is a property of a series circuit. To analyze this circuit (finding the current, power, etc.), it is first neces-sary to reduce this circuit. The first step will be to substitute all the com-ponents of the same type by a single component equivalent to all those. This is what is always pursued (for parallel and combination circuits, as well). In this chapter we discuss only finding the equivalent circuit for resis-tors.
eBook - ePub- Adrian Waygood(Author)
- 2018(Publication Date)
- Routledge(Publisher)
Chapter 11 Series, parallel and series-parallel circuitsObjectives
On completion of this chapter, you should be able to- recognise a series circuit, a parallel circuit and a series-parallel circuit.
- recognise and interpret voltage and current ‘sense’ arrows.
- explain Kirchhoff’s Voltage Law.
- explain Kirchhoff’s Current Law.
- calculate the total resistance of a series resistive circuit.
- calculate the current flow through a series resistive circuit.
- calculate the voltage drop appearing across each resistor in a series resistive circuit.
- explain the potential hazard of an open circuit in a series circuit.
- calculate the total resistance of a parallel resistive circuit.
- calculate the current flow through each branch of a parallel resistive circuit.
- calculate the voltage drop appearing across each resistor in a parallel resistive circuit.
- explain the major advantages of a parallel circuit.
- calculate the total resistance of a series-parallel resistive circuit.
- calculate the current flow through each resistor in a series-parallel resistive circuit.
- calculate the voltage drop appearing across each resistor in a series-parallel resistive circuit.
- calculate the voltage drop along conductors supplying a load.
Introduction
In order for charge carriers to flow, there must be a continuous external conducting path, called a circuit , between the terminals of a source of electromotive force (e.g. a battery, generator, etc.) and a load (e.g. a lamp, electric heater, etc.). This continuous ‘conducting path’ is termed a closed circuit . If there is a break anywhere in this conducting path, then there can be no current and it’s termed an open circuit .Circuits are categorised according to the way in which they are connected. There are four
eBook - PDF- Michael Neidle(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Chapter 4 D C . CIRCUITS In order to deal in a confident manner with more involved circuits, students should make a point of fully understanding simple Series and Parallel Circuits. We commence with the 'rules of the game', but as in most parts of this work plenty of practice from earlier years' work will aid in achieving a permanent grasp of the subject. Fig. 4.1. The series circuit. 4.1. Resistors in Series The supply voltage Vis obviously equal to the sum of the potential difference across each resistor (Fig. 4.1): Voltage law V=V l +V 2 +V 3 As the same current flows through each of the resistors, V x = IR l V 2 = IR 2 V= / Ä 1 + / R 2 + IR 3 = /(R 1 +K 2 +R 3 ) But V = IR where R = total resistance IR = P 1 + R 2 + R 3 ) thus R = R l +R 2 +R 3 61 and V, = IR, 62 ELECTRICAL INSTALLATION TECHNOLOGY Example 4.1 Four similar indicator filament lamps, each rated at 5 W, 50 V, are connected in series across a 200 V supply. What is the total current taken from the supply? After a period of operation, one of the lamps fails and becomes open-circuited. Explain how a voltmeter may be used to find which lamp has failed, stating clearly what readings would be expected on the voltmeter. The only replacement lamp available is one rated at 2-5 W 50 V. What would be the voltages across this lamp and each of the other lamps if this replacement were used in the circuit, and what would be the probable result ? [T] Power in Substituting By transposition watts = voltage x current P=VI I · ' -S V 2 Thus, resistance of each of the 5 W, 50 V lamps 50x50 ~ 5 Total resistance of the 4 lamps Current in circuit 200 V 2000 Ω = 500Ω = 2000 Ω = 01 A Since an open-circuited lamp does not allow any current to pass in a series circuit Reading by voltmeter across good lamps = zero Reading across faulty lamp = practically full voltage of 200 V This is because the voltmeter would have a high resistance, being 1000 Ω/V for a good instrument, i.e.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
20.7 | Parallel Wiring 497 Parallel wiring is very common. For example, when an electrical appliance is plugged into a wall socket, the appliance is connected in parallel with other appliances, as in Figure 20.19, where the entire voltage of 120 V is applied across each one of the devices: the television, the stereo, and the light bulb (when the switch is turned on). The presence of the unused socket or other devices that are turned off does not affect the operation of those devices that are turned on. Moreover, if the current in one device is interrupted (perhaps by an opened switch or a broken wire), the current in the other devices is not interrupted. In contrast, if household appliances were connected in series, there would be no current through any appliance if the current in the circuit were halted at any point. When two resistors R 1 and R 2 are connected as in Figure 20.18, each receives current from the battery as if the other were not present. Therefore, R 1 and R 2 together draw more current from the battery than does either resistor alone. According to the definition of resis- tance, R 5 V/I, a larger current implies a smaller resistance. Thus, the two parallel resistors behave as a single equivalent resistance that is smaller than either R 1 or R 2 . Figure 20.20 returns to the water-flow analogy to provide additional insight into this important feature of parallel wiring. In part a, two sections of pipe that have the same length are connected in parallel with a pump. In part b these two sections have been replaced with a single pipe of the same length, whose cross-sectional area equals the combined cross-sectional areas of section 1 and section 2. The pump (analogous to a voltage source) can push more water per second (analogous to current) through the wider pipe in part b (analogous to a wider wire) than it can through either of the narrower pipes (analogous to narrower wires) in part a.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Moreover, if the current in one device is interrupted (perhaps by an opened switch or a broken wire), the current in the other devices is not interrupted. In contrast, if household appliances were connected in series, there would be no current through any appliance if the current in the circuit were halted at any point. When two resistors R 1 and R 2 are connected as in figure 20.18, each receives current from the battery as if the other were not present. Therefore, R 1 and R 2 together draw more current from the battery than does either resistor alone. According to the definition of resistance, R = V /I, a larger current implies a smaller resistance. Thus, the two parallel resistors behave as a single equivalent resistance that is smaller than either R 1 or R 2 . Figure 20.20 returns to the water‐flow analogy to provide additional insight into this important feature of parallel wiring. In part a, two sections of pipe that have the same length are connected in parallel with a pump. In part b these two sections have been replaced with a single pipe of the same length, whose cross‐sectional area equals the combined cross‐sectional areas of section 1 and section 2. The pump (analogous to a voltage source) can push more water per second (analogous to current) through the wider pipe in part b (analogous to a wider wire) than it can through either of the narrower pipes (analogous to narrower wires) in part a. In effect, the wider pipe offers less resistance to the flow of water than either of the narrower pipes offers individually. 552 Physics FIGURE 20.20 (a) Two equally long pipe sections, with cross‐sectional areas A 1 and A 2 , are connected in parallel to a water pump. (b) The two parallel pipe sections in part a are equivalent to a single pipe of the same length whose cross‐sectional area is A 1 + A 2 .
eBook - PDFCircuit Analysis with PSpice
A Simplified Approach
- Nassir H. Sabah(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
• The following are the features of a parallel con- nection of circuit elements: 1. One end of each element is connected to a common node, whereas the other end of each of these elements is connected to another common node. 2. Any two paralleled elements form a mesh or a loop that does not include any additional elements. 3. The same voltage appears across all the par- allel-connected elements, so KVL is auto- matically satisfied. 4. Currents add algebraically at the nodes between which the elements are paralleled. • The series and parallel connections can be used to build resistive circuits of any desired complexity. • A problem-solving approach, ISDEPIC, can be applied as a series of steps that can be very help- ful in analyzing a given circuit and arriving at the solution systematically and efficiently. Problem-Solving Tips 1. The solution to any circuit problem can be checked by making sure that Ohm’s law is satis- fied for every resistor, KCL is satisfied at every node, and KVL is satisfied around every mesh. 2. If a circuit has N essential nodes, then after writ- ing KCL for (N − 1) essential nodes, KCL at the remaining essential node should be automati- cally satisfied if KCL was written correctly at the other nodes. 3. Always mark on the circuit diagram the direc- tions of currents of interest and the polarities of voltages of interest, bearing in mind that the current through an ideal resistor is in the direc- tion of the voltage drop across the resistor. 4. Circuits having only two essential nodes can generally be analyzed by applying KCL at either node. 5. Controlling currents or voltages of dependent sources are often convenient to use as unknown variables in analyzing circuits. 6. A circuit with rather awkward-looking connec- tions can be redrawn, after labeling of nodes, for easier visualization of the connections. Problems Apply ISDEPIC and verify solutions by PSpice simulation whenever feasible.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The presence of the unused socket or other devices that are turned off does not affect the operation of those devices that are turned on. Moreover, if the current in one device is interrupted (perhaps by an opened switch or a broken wire), the current in the other devices is not interrupted. In contrast, if household appliances were con- nected in series, there would be no current through any appliance if the current in the circuit were halted at any point. When two resistors R 1 and R 2 are connected as in Figure 20.18, each receives current from the battery as if the other were not present. Therefore, R 1 and R 2 together draw more current from the battery than does either resistor alone. According to the definition of resistance, R = V/I, a larger current implies a smaller resistance. Thus, the two parallel resistors behave as a single equivalent resistance that is smaller than either R 1 or R 2 . Figure 20.20 returns to the water-flow analogy to provide additional insight into this important feature of parallel wiring. In part a, two sections of pipe that have the same length are connected in parallel with a pump. In part b these two sections have been replaced with a single pipe of the same length, whose cross- sectional area equals the combined cross-sectional areas of section 1 and section 2. The pump (analogous to a voltage source) can push more water per second (analogous to current) through the wider pipe in part b (analogous to a wider wire) than it can through either of the narrower pipes (analogous to narrower wires) in part a. In effect, the wider pipe offers less resistance to the flow of water than either of the narrower pipes offers individually. As in a series circuit, it is possible to replace a parallel combination of resistors with an equivalent resistor that results in the same total current and power for a given voltage as the original combination.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
20.8 | Circuits Wired Partially in Series and Partially in Parallel 559 Check Your Understanding (The answers are given at the end of the book.) 13. A car has two headlights, and their power is derived from the car’s battery. The filament in one burns out, but the other headlight stays on. Are the headlights connected in series or in parallel? 14. Two identical light bulbs are connected to identical batteries in two different ways. In method A the bulbs are connected in parallel, and the parallel combination is connected between the one battery’s terminals. In method B the bulbs are connected in series, and the series combination is connected between the other battery’s terminals. What is the ratio of the power supplied by the battery in method A to the power supplied in method B? (a) 1 4 (b) 4 (c) 1 2 (d) 2 (e) 1 20.8 | Circuits Wired Partially in Series and Partially in Parallel Often an electric circuit is wired partially in series and partially in parallel. The key to determining the current, voltage, and power in such a case is to deal with the circuit in parts, with the resistances in each part being either in series or in parallel with each other. Example 12 shows how such an analysis is carried out. EXAMPLE 12 | A Four-Resistor Circuit Figure 20.23a shows a circuit composed of a 24-V battery and four resistors, whose resistances are 110, 180, 220, and 250 V. Find (a) the total current supplied by the battery and (b) the volt- age between points A and B in the circuit. Reasoning The total current that is supplied by the battery can be obtained from Ohm’s law, I 5 V/R, where R is the equiva- lent resistance of the four resistors. The equivalent resistance can be calculated by dealing with the circuit in parts. The volt- age V AB between the two points A and B is also given by Ohm’s law, V AB 5 IR AB , where I is the current and R AB is the equivalent resistance between the two points.
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