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Fundamentals of Electrical Circuits

This figure highlights automotive circuits, equivalent electrical circuits, electrical vehicle battery packs, various representations of electrical systems, resistors, KVL and KCL, parallel and series circuits, Wheatstone bridge circuits, practical voltage and current sources, measurement of current and voltage, power measurement, circuit branches, nodes, loops, and meshes.

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Fundamentals of Electrical Circuits

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  1. 2 C H A P T E R Fundamentals of Electrical Circuits

  2. Figure 2.4 (a) Automotive circuits

  3. I batt I I I I I I head tail start fan locks dash + V batt – (b) Figure 2.4 (b) Equivalent electrical circuit

  4. V V V batt1 batt2 battn 12 V 12 V 12 V 12 V 12 V DC-AC converter (electric drive) AC motor (a) Figure 2.8 (a) Electrical vehicle battery pack

  5. v v v batt2 batt3 batt31 + – + – + – + + Power converter and motor v v batt1 drive – – Figure 2.8 (b)Illustration of KVL (b)

  6. i i + + _ + v Source V v Load R S – – + – Headlight Car battery i Power flow (a) Conceptual (b) Symbolic (circuit) (c) Physical representation representation representation Figure 2.10 Various representations of an electrical system

  7. i (amps) 0.5 0.4 0.3 0.2 0.1 (volts) – 60 – 50 – 40 – 30 – 20 – 10 0 10 20 30 40 50 60 v – 0.1 Current meter – 0.2 i – 0.3 + Variable v – 0.4 voltage source – – 0.5 Figure 2.18 Volt-ampere characteristic of a tungsten light bulb

  8. i i + l R v 1/ R l R = A – A v Physical resistors Circuit symbol i-v characteristic with resistance R. Typical materials are carbon, metal film. Figure 2.20 The resistance element

  9. b b b b 4 3 2 1 Color bands black 0 blue 6 brown 1 violet 7 red 2 gray 8 orange 3 white 9 yellow 4 silver 10% green 5 gold 5% b Resistor value = ( b b ) 10 ; 3 1 2 b = % tolerance in actual value 4 Figure 2.22 Resistor color code

  10. R + v – + + _ v R 1.5 V i – – v + The current i flows through each of + the four series elements. Thus, by 1.5 = v v v + 1 2 3 KVL, R N R n R EQ R 3 series resistors are equivalent to N R 2 a single resistor equal to the sum of the individual resistances. R 1 Figure 2.30

  11. KCL applied at this node + i i i 1 2 3 R R R R R R 1 2 3 n N EQ i R R R v S 1 2 3 – resistors in parallel are equivalent to a single equivalent N The voltage v appears across each parallel resistor with resistance equal to the inverse of the sum of the inverse resistances. element; by KCL, i i = + i + i S 1 2 3 Figure 2.32 Parallel circuits

  12. c R R 1 3 + v v v _ a b S a b R R 2 x d (a) c R R 1 3 + v _ a v v b S a b R R x 2 d (b) Figure 2.36 Wheatstone bridge circuits

  13. F c i i a b R R 1 3 + R , R bonded v v v 2 3 S a b to bottom surface – R R 2 4 Beam cross section h w d Figure 2.37 A force-measuring instrument

  14. i r S S + Practical voltage + v v R _ S L L source – v S i = S r + R S L v S i = lim S r R S 0 L i r S max S + v + v _ S L The maximum (short circuit) – current which can be supplied by a practical voltage source is v i S = S max r S Figure 2.38 Practical voltage source

  15. A model for practical current + sources consists of an ideal source in parallel with an internal i v r R S S S L resistance. – Maximum output + voltage for practical i v r current source with S S S open-circuit load: – v = i r S max S S Figure 2.39 Practical current source

  16. R R 1 1 A + + v v R A _ _ S S 2 R i i 2 Symbol for A series Circuit for the measurement ideal ammeter circuit of the current i Figure 2.41 Measurement of current

  17. R R 1 1 + + + + + v v v R v R v _ _ V V S 2 2 2 2 2 S – – – i i A series Ideal Circuit for the measurement circuit voltmeter of the voltage v 2 Figure 2.42 Measurement of voltage

  18. r V m Practical voltmeter A r m Practical ammeter Figure 2.43 Models for practical ammeter and voltmeter

  19. i R R 1 1 A W + + + + v v v v R R V _ _ S S 2 2 2 2 – – Measurement of the power Internal wattmeter connections dissipated in the resistor R : 2 P v i = 2 2 Figure 2.44 Measurement of power i

  20. i + A Branch Branch v R voltage current r m – A branch b Ideal A battery Practical resistor ammeter Examples of circuit branches Figure 2.45 Definition of a branch a

  21. Node a Node c Node a i v S S Node Node b Node b Examples of nodes in practical circuits Figure 2.47 Definition of a node

  22. Note how two different loops in the same circuit may in- clude some of the same ele- ments or branches. R R R i 1 2 S v Loop 1 Loop 2 S 3-loop circuit (How many nodes in 1-loop circuit this circuit?) Loop 3 Figure 2.48 Definition of a loop

  23. How many loops can you identify in this four-mesh circuit? (Answer: 14) R R 4 3 Mesh 3 Mesh R 1 4 + R Mesh 5 Mesh v R 3 1 S 2 i _ S Figure 2.49 Definition of a mesh

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