Physics
Current Sources in Parallel
Current sources in parallel are two or more current sources connected to a common load. The total current supplied to the load is the sum of the individual currents supplied by each source. The voltage across each source is the same, but the current through each source may be different.
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7 Key excerpts on "Current Sources in Parallel"
- 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 - PDFEssentials of Advanced Circuit Analysis
A Systems Approach
- Djafar K. Mynbaev(Author)
- 2024(Publication Date)
- Wiley(Publisher)
It must be pointed out that the above discussion refers to the ideal sources. 1.5.2 Series and Parallel Sources, Ideal and Real Sources, and Source Transformation Three more points are worth consideration. 1) First, the voltage sources can be connected in series, and the current sources can be connected in parallel. These configurations enable us to increase the output of the sources. Figures 1.23a Figure 1.22 Current sources: a) Independent source; b) voltage-controlled current source; c) current- controlled current source. (Sources are shown in Multisim notations.) 1.5 Sources (Inputs, Excitations, or Drives) 57 and 1.23b illustrate the concept. Two voltage sources connected in series supply the sum of their voltages to the load circuit, as shown in Figure 1.23a. Two current sources connected in parallel feed the load circuit with the sum of their currents, as illustrated in Figure 1.23b. However, these summation rules are valid only for sources; series and parallel connections of the passive components (resistors, capacitors, and inductors) obey different regulations, as dis- cussed in Section 1.3. Another particularity of the source connections is that the voltage sources must be never connected in parallel, and the current sources cannot be wired in series. Question Can the controlled (dependent) voltage sources be connected in series? Controlled Current Sources in Parallel? 2. The second point is about the difference between an ideal and a real (practical) source. The ideal sources are shown in Figures 1.20 through 1.23 and described in the preceding part of this section. In reality, however, every source includes its internal resistance, R int ( ) Ω . Figure 1.24a shows that an internal resistor, R int 1 , is connected in series in a practical (real) voltage source. Figure 1.24b demonstrates that resistor R int 2 is wired in parallel in a practical (real) current source. The load circuit’s viewpoint at the sources is shown in Figure 1.24c.
eBook - PDFAnalog BiCMOS Design
Practices and Pitfalls
- James C. Daly, Denis P. Galipeau(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
chapter 3 Current Sources Current sources are the foundation of circuit design in microelectronics. Current sources provide biasing for circuit operation. They serve as out- put drivers. They serve as load elements in amplifier input stages. Even logic gates can be modeled as a collection of variable current sources. Analysis of circuits in proceeding chapters will often show a resistance biasing the block under analysis. Current mirrors are used almost ex- clusively for this purpose in microelectronics. Current sources offer the advantages of smaller size, higher accuracy and can be designed to pro- vide temperature coefficients of current as needed. However, resistors can and do serve well as current sources in some instances. Let us first consider the characteristics of an ideal DC current source as provided in circuit simulators such as SPICE. Constant current of any value is provided at all times. Infinite output impedance means there is no change in the source current value due to changes in the output node voltage. The source has infinite compliance, and will provide the specified current regardless of the voltage across the source. An ideal current source can either sink or source current. The polarity of the specified DC current and the nodal connection of the current source to the rest of the circuit determine how the source behaves. (Most simulators have an ideal current source with two nodes: positive and negative. Positive current flow in the ideal source is defined as flowing into the positive node and out of the negative node.) Unfortunately, physical constraints apply in the real world of semicon- ductors, and real current sources fall short of perfection. Current provided by integrated circuit current sources are constant within some tolerance, and the value of current depends on limita- tions of device size, power dissipation and process Early voltages.
eBook - PDF- Giovanni Saggio(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Ideal current sources cannot be connected in series. 4.5.3 Non-Ideal Voltage and Current Sources The model given from ideal voltage and current sources, although used often, does not exactly match those that are the real ones. In fact, ideal sources are mathemati-cal abstractions, and their model can also lead to certain incongruities. For example, an ideal voltage source can provide infinite current with non-zero voltage difference, and an ideal current source can provide infinite voltage difference with non-zero current, so either device is theoretically capable of delivering infinite power! We know that for two devices in a parallel topology, the voltage across them is the same, but then what happens if those two devices are two ideal voltage sources, each of them providing a voltage of different value? We will have the paradox that the voltage should be the same, but each of the sources can impose a different one. An analogous paradox is for two current sources in series, each of them pro-viding a different current value. What will be the real amount of current flowing through them? These incongruities find solutions when considering the independent sources as a real model that takes into account their unwanted but unavoidable internal electrical resistance (as defined in Section 3.9 of Chapter 3). Since these devices I S (a) I S (b) V I (c) FIGURE 4.41 (a), (b) Current source symbols, (c) I-V characteristic of an ideal current source. i s (a) i s (a) (b) i s (c) FIGURE 4.42 Some commonly adopted symbols for the variable current source. Two-Terminal Components 119 are made of materials with non-zero resistive value, their internal resistance can-not be null. So, this internal resistance will be such to distinguish the ideal model from the real one. For the voltage source this means that it may not always provide a voltage of constant value, at any time and for every load.
eBook - PDFLinear Circuit Theory
Matrices in Computer Applications
- Jiri Vlach(Author)
- 2016(Publication Date)
- Apple Academic Press(Publisher)
The amount is P = 2 × 1.5 = 3 W . The power delivered by the left source is exactly equal to the power consumed by the resistor and the other source. Example 4. A parallel connection of a voltage and current source is in Fig. 1.5.4. Calculate the powers delivered and consumed by the respective elements. Due to the voltage source, the voltage across the resistor must be 6 V and the current through the resistor must be, due to the Ohm’s law, I 6 2 3 R = = A . The current source is supplying 10 A . Three amperes will be forced through the resistor, the rest must flow through the voltage source, from + to −. The powers are distributed as follows: The current source delivers P = 6 × 10 = 60 W . Of this the resistor consumes P = 3 × 6 = 18 W while the voltage source consumes P = 6 × 7 = 42 W . As always, the power delivered is equal to the power consumed. 1.6. KIRCHHOFF’S LAWS The laws discovered by Kirchhoff are fundamental to the theory of electricity. They are valid in any situation, even if the elements are nonlinear or time varying. FIGURE 1.5.3 Network with two voltage sources. FIGURE 1.5.4 Network with current and voltage source. 20 Basic Concepts 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.6.1. Kirchhoff Current Law The Kirchhoff current law ( KCL ) states that the sum of currents flowing away from a node is zero . The definition remains valid if we replace the words away from by the word to . A node is a point where we connect several elements and one such case is shown in Fig. 1.6.1a. Since the node is only a connection of wires, it is easily understood that it cannot store electrons and thus any amount of electrons flowing into the node through some of the connecting lines must also leave through some other lines. In the statement of the law we used the word away because in this book we will consider a current flowing away from a node as having positive direction. In Fig. 1.6.1a we have five elements connected to the central node.
eBook - PDF- A. Henderson(Author)
- 2014(Publication Date)
- Arnold(Publisher)
In that case, however, the source currents cannot be calculated. Two current sources in series are forbidden if the sum of the source strengths is not zero (for in this case KirchhofF s current law for the node between the two sources) is not valid. Two current sources in series are not forbidden if the sum of the source strengths is zero. In that case the source voltages cannot be calculated. In network theory it often happens that there is analogy between two formulas, between two elements or between two circuits. For instance, one Kirchhoff's law turns into the other if one substitutes voltage for current and vice versa. We therefore say that the current law is the dual of the voltage law and vice versa. The dual character is also found in • voltage - current • open nodes - short circuit • resistance - conductance In the following chapters we shall often meet this phenomenon of duality. 1.3 Energy and power The voltage V A B between two points A and B is defined as the work needed to move a unit charge (1 C concentrated in a point) from point B to point A. If the charge is Aq the work is therefore AW = (V A - V B )Aq = V AB Aq, (1.14) in which VA and VB are the potentials of the points A and B. If VAB is constant (d.c.) and if the work is done in a time At, the average power is p _ A W _ Aq r At v At ' in which V = VAB-For At -> 0 we obtain P = VI. (1.15) So the power, in the case of d.c, is the product of voltage and current. Energy is expressed in joule (J), power in watt (W). Power can be consumed or supplied. If a current I flows through a network N with two terminals (also called a one-port) and if the polarity of the voltage V is such that I flows from + to - the power consumed is positive (Figure 1.11). 18 d.c. currents and d.c. voltages The voltage source transports (positive) charge from minus to plus and so delivers electrical energy to N (this energy is supplied by the chemical or mechanical system outside the network).
eBook - PDF- Michael Neidle(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
4.3. Parallel Circuits In the basic parallel circuit (Fig. 4.5), the main current I is the sum of the individual branch currents. Current law / = / 1 + / 2 + / 3 Since the voltage V is common and I = — V _ V V V where R is the equivalent ^ ^ ^ ^ resistance of the group 66 ELECTRICAL INSTALLATION TECHNOLOGY Fig. 4.5. Currents through resistors connected in parallel. I* It Ri I 2 R 2 I3 R3 -»»—1 h Dividing through by V, K /^! K 2 #3 Occasionally, this reciprocal form can be usefully replaced by J J / 2 ' ί | Λ 3 T /V2/V3 The expression above is obtained through using the product R l R 2 R 3 as an L.C.M. More often, for two resistors in parallel, the expression R = KjR 2 Ä!+R 2 makes for easier working. For series-parallel circuits, resistors in parallel should be seen as a single group in series with other resistors. Example 4.3 Four resistors, AB, BC, AD and DC, are connected together to form a closed square ABCD. The known resistance values are: AD 12 Ω, AB 35 Ω, and DC 12 Ω. A d.c. supply of 120 V is connected to A and C so that current enters the combination at A and leaves at C. A high-resistance voltmeter is connected between B and D and, whilst carrying negligible current, registers a voltage drop of 10 V from B to D. (a) Calculate the value of the resistance BC, and the total current taken from the supply. (b) Calculate also the value of BC, such that the potential difference between B and D is in the reverse direction i.e. from D to B. [C] D.C. CIRCUITS 67 -120V Fig. 4.6. Circuit conditions of balanced bridge. (a) The circuit conditions are given in Fig. 4.6. The supply current / enters the junction at A and splits up into the currents l x and I 2 as shown; also the network consists of two parallel branches each comprising two resistors in series, since negligible current passes through the voltmeter. As the resistors AD and DC are equal and form one parallel branch, a p.d. of 60 V must exist between the ends of these resistors.
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