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= 1023 carriers
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= 5033 103 C
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Fundamentals of Electric Circuits
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To compute the current, we consider the velocity of the charge carriers, and the charge density per unit length of the conductor: Current = Carrier charge density per unit length Carrier velocity I= Q C L m u m = 5033 103 s C m 199 10 6 m =1 A s
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Comments: Charge carrier density is a function of material properties Carrier velocity
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i = Current flowing in closed circuit
+ 15 V 15 V battery
Light bulb
Figure 22 A simple electrical circuit
In order for current to ow there must exist a closed circuit Figure 22 depicts a simple circuit, composed of a battery (eg, a dry-cell or alkaline 15-V battery) and a light bulb Note that in the circuit of Figure 22, the current, i, owing from the battery to the light bulb is equal to the current owing from the light bulb to the battery In other words, no current (and therefore no charge) is lost around the closed circuit This principle was observed by the German scientist G R Kirchhoff 4 and is now known as Kirchhoff s current law (KCL) Kirchhoff s current law states that because charge cannot be created but must be conserved, the sum of the currents at a node must equal zero (in an electrical circuit, a node is the junction of two or more conductors) Formally:
in = 0
Kirchhoff s current law
(25)
Node 1 i1 i2 i3
+ Battery 15 V i Node 2 Illustration of KCL at node 1: i + i1 + i2 + i3 = 0
The signi cance of Kirchhoff s current law is illustrated in Figure 23, where the simple circuit of Figure 22 has been augmented by the addition of two light bulbs (note how the two nodes that exist in this circuit have been emphasized by the shaded areas) In applying KCL, one usually de nes currents entering a node as being negative and currents exiting the node as being positive Thus, the resulting expression for node 1 of the circuit of Figure 23 is: i + i1 + i2 + i3 = 0 Kirchhoff s current law is one of the fundamental laws of circuit analysis, making it possible to express currents in a circuit in terms of each other; for example, one can express the current leaving a node in terms of all the other currents at the node The ability to write such equations is a great aid in the systematic solution of large electric circuits Much of the material presented in 3 will be an extension of this concept
Figure 23 Illustration of Kirchhoff s current law
4 Gustav
Robert Kirchhoff (1824 1887), a German scientist, who published the rst systematic description of the laws of circuit analysis His contribution though not original in terms of its scienti c content forms the basis of all circuit analysis
Part I
Circuits
EXAMPLE 22 Kirchhoff s Current Law Applied to an Automotive Electrical Harness
Problem
Figure 24 shows an automotive battery connected to a variety of circuits in an automobile The circuits include headlights, taillights, starter motor, fan, power locks, and dashboard panel The battery must supply enough current to independently satisfy the requirements of each of the load circuits Apply KCL to the automotive circuits
Ibatt Ihead + Vbatt Itail Istart Ifan Ilocks Idash
Figure 24 (a) Automotive circuits (b) equivalent electrical circuit
Solution
Known Quantities: Components of electrical harness: headlights, taillights, starter motor, fan, power locks, and dashboard panel Find: Expression relating battery current to load currents Schematics, Diagrams, Circuits, and Given Data: Figure 24 Assumptions: None
2
Fundamentals of Electric Circuits
Stereo wiring Radio wiring Ash tray lamp Glove box lamp
Printed circuit board connectors
To door courtesy switch To heater blower motor resistor To A/C blower motor resistor To right front door resistor Heater blower motor feed Cigarette lighter To key-in buzzer To key-lamp To wiper switch To ignition switch lamp To intermittent wipe To turn signal switch To accessory lamps To headlamp dimmer switch To ignition switch To stop lamp switch To speed control switch wiring To speed control brake wiring To speed control clutch switch To speed control servo Headlamp switch Heated rear window switch and lamp Rear wipe and wash switch and lamp l body M-Z 44 Lamp Lifegate release l body M-Z24 Ground Fuse block To stereo speakers MZ24 To left door speakers To left door courtesy switches To rear wipe wash To heated rear window To hatch release To body wiring Bulkhead disconnect Automotive wiring harness (c)
Figure 24 (c) Automotive wiring harness Copyright c 1995 by Delmar Publishers Copyright c 1995 1997 Automotive Information Center All rights reserved
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