ELECTRICAL THEORY. Ideal Basic Circuit Element


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1 ELECTRICAL THEORY PROF. SIRIPONG POTISUK ELEC 106 Ideal Basic Circuit Element Has only two terminals which are points of connection to other circuit components Can be described mathematically in terms of current and voltage Cannot be subdivided into other elements A lumpedparameter model of a realizable physical component 1
2 Terminology A circuit  an interconnection of electrical elements providing one or more closed paths A planar circuit  can be drawn on a plane with no crossing branches A nonplanar circuit  cannot be drawn without crossover branches Planar Circuit 2
3 Terminology A node a point or junction at which two or more elements come together (indicated by a dot) A trivial node a node with only two elements An essential node a nontrivial node (three or more elements) A port a convenient pairing of two terminals not necessarily from the same element A path a trace of adjoining basic elements with no elements included more than once Terminology A branch  a path that connects two nodes A basic branch  a single element An essential branch a path which connects two essential nodes without passing through an essential node A loop a path whose ending node is the same as the beginning node (a closed path) A mesh  a loop that does not enclose any other loops 3
4 Series & Parallel Connection Two or more elements are connected in series if a pair of contiguous elements shares a single trivial node and all of them are chainconnected end to end they carry the same current Two or more elements are connected in parallel if they exclusively share a single node pair they have the same voltage across their terminals Example 4
5 Kirchhoff s Laws Two experimental laws formulated by a German physicist, Gustav Robert Kirchhoff in 1847 Impose constraints on the relationship between the terminal voltages and currents of interconnected circuit elements Kirchhoff s Current Law (KCL) Based on the law of conservation of electric charges The algebraic sum of all the currents at any node in a circuit equals zero The sum of the currents entering a node is equal to the sum of the currents leaving that node 5
6 Example Example Use KCL to find the branch currents I 1 to I 4 6
7 Kirchhoff s Voltage Law (KVL) Based on the law of conservation of electric energy The algebraic sum of all voltages around a closed path (or loop) in a circuit equals zero Sum of voltage drops = Sum of voltage rises Can be applied by taking either a clockwise or a counterclockwise trip around the loop The sign of each voltage is the polarity of the terminal encountered first Example 7
8 Example Use KVL to obtain the voltages v 1 to v 3 Example Sum the voltages around each designated path in the circuit shown 8
9 Resistance A characteristic behavior or physical property of all materials to resist the flow of electric charge or current Denoted by R and measured in ohms ( ) R = ρ l A = material resistivity ( m) l = length (m) A = crosssectional area (m 2 ) Material Resistivity ( m) Usage Silver Conductor Copper Conductor Aluminum Conductor Gold Conductor Carbon Semiconductor Germanium Semiconductor Silicon Semiconductor Paper Insulator Mica Insulator Glass Insulator Teflon Insulator 9
10 Resistor Circuit element used in modeling the currentresisting behavior of a material Circuit symbols: Ohm s Law The voltage across a resistor is directly proportional to the current flowing through it v = ir or R = v i where R is the proportionality constant or resistance 1 = 1 V/A Positive current flows in the direction of voltage drop 10
11 Simple Resistive Circuit Example Use Ohm s law and Kirchhoff s laws to find the value of R in the circuit shown. 11
12 Power Relationship The power dissipated in a resistor is a nonlinear function of either current or voltage p = vi = i 2 R = v2 Since R > 0, p is always positive, R is a passive element, incapable of generating energy R Practical Resistors Usually made from metallic alloys and carbon compounds Ideal resistor is the simplest passive element with linear vi characteristic and obeying Ohm s Law Practical resistors may exhibit nonlinear behavior under certain conditions (i.e., very high or low voltages and currents Designated with power rating reflecting different types of materials used in its construction 12
13 Short Circuit When two points in a circuit are connected by an ideal conductor (a wire), they are said to be shorted together. An ideal conductor is called a short circuit and can be thought of as an element with R = 0. The voltage across the two points is zero while the current flow can be anything. 13
14 Open Circuit When two points in a circuit are not connected, an open circuit is said to exist between them. An open circuit can be thought of as an element with R =. The voltage across the two points can be anything while the current flow is zero. Ideal Switch Electrically, an ideal switch is a twostate device (ON or OFF) Offers no resistance to the current when ON while offers infinite resistance when OFF 14
15 Series Resistances Linear resistors possess the additivity property Series Resistances The equivalent resistance of any part of a circuit consisting of a number of resistors connected in series is the sum of the individual resistances R eq = R 1 + R R N = In terms of conductances, 1 = = G eq G 1 G 2 G N N i=1 N R i 1 G i i=1 15
16 Parallel Resistances Parallel Resistances The equivalent conductance of any part of a circuit consisting of a number of resistors connected in parallel is the sum of the individual conductances G eq = G 1 + G G N = In terms of resistances, 1 = = R eq R 1 R 2 R N N i=1 N G i 1 R i i=1 16
17 Parallel Resistances For N = 2, G eq = G 1 + G 2 In terms of resistances, 1 R eq = 1 R R 2 R eq = R 1 R 2 R 1 + R 2 and R eq is always less than the smaller of the two resistors SeriesParallel Combinations 1) Connect an ohmmeter across the viewing port or terminals where R eq is to be obtained. 2) Label all the nodes 3) Examine how the resistors are connected to each node or a node pair by 3.1 identify a trivial node series connection 3.2 identify a node pair parallel connection 4) Combine those resistors and repeat step (3) until a single resistor is connected to an ohmmeter 17
18 Example Obtain an equivalent resistance of the following network of resistors 18
19 Example 19
20 Mesh Currents Exist only in the perimeter of the mesh Selected in the same direction (CW or CCW) for all meshes Imaginary current circulating all the way around the mesh Mesh Current Example Write the mesh current equations for the following circuit 20
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