ECE 1311: Electric Circuits. Chapter 2: Basic laws

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1 ECE 1311: Electric Circuits Chapter 2: Basic laws

2 Basic Law Overview Ideal sources series and parallel Ohm s law Definitions open circuits, short circuits, conductance, nodes, branches, loops Kirchhoff's law Voltage divider and series resistors Current divider and parallel resistors Wye-Delta transformations

3 Ideal Voltage Source Ideal voltage source in series can be added Ideal voltage source in parallel = NO GOOD ecall: ideal voltage source guarantee the voltage between two terminals is at the specified potential (voltage) BOOM

4 Ideal Current Source Ideal current source cannot be connected in series Ideal current source in parallel can be added ecall: ideal current guarantee the current flowing through source is at the specified value ecall: Current entering a circuit must be equal to the current leaving the circuit BOOM

5 esistance All material resist the flow of current given by l A = resistance of an element in ohms p = resistivity of material in ohm-meters l = length of material in meters A = cross sectional area of material in meter 2

6 Ohm s Law (1) Ohm s law states that the voltage across a resistor is directly proportional to the current flowing through the resistor. v i Only material with linear relationship satisfy Ohm s law (note the PSC)

7 Ohm s Law (2) Two extreme possible values of : 0 (zero) and (infinite) are related with two basic circuit concepts: short circuit and open circuit. Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance and is measured in mhos or siemens. i G 1 v The power dissipated by a resistor: p vi 2 v Power absorbed by is always positive i 2

8 Practice 2.1

9 Short circuit An element (or wire) with = 0 is called a short circuit An ideal voltage source with V = 0 is equivalent to a short circuit Since v = i and = 0, v = 0 regardless of i ecall: cannot connect voltage source to a short circuit

10 Open circuit An element with = is called the open circuit Often represented by a wire with an open connection An ideal current source I = 0A is also equivalent to an open circuit ecall: cannot connect current source to an open circuit

11 Formalization For this course, networks and circuits will be used interchangeably Networks are composed of nodes, branches and loops

12 Nodes, Branches and Loops A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches. A loop is any closed path in a circuit. A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology: b l n 1

13 Practice 2.2 How many branches, nodes and independent loops are there?

14 Practice 2.3 How many branches, nodes and loops are there?

15 Overview on Kirchhoff s Law It s the foundation of circuit analysis There are two - Kirchhoff s current law (KCL) and Kirchhoff s voltage law (KVL) It tell us how the voltage and current are related within a circuit element are related

16 Kirchhoff s Current Law (1) Kirchhoff s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero. i.e. the sum entering a node is equal to the sum leaving a node based on the law on conservation charge

17 Kirchhoff s Current Law (2) KCL also apply at the boundary

18 Practice 2.4 Given that essential node is the point between 3 or more branches,

19 Kirchhoff s Voltage Law (1) Kirchhoff s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. Based on the conservation of energy

20 Practice 2.5

21 Practice 2.6 Apply KVL to find the value I

22 Summary on Ohm s Law, KCL and KVL Ohm s Law KCL KVL v i I V n n 0 0 These law alone are sufficient to analyze many circuits

23 Practice 2.7 Find v 2, v 6 and v I

24 Practice 2.8 Find i 0 and v 0

25 Practice 2.9

26 esistor Circuit Overview esistors in series esistors in parallel Voltage dividers Current dividers Wye-Delta transformation

27 esistors in series

28 esistors in Parallel (1)

29 esistors in Parallel (2)

30 Voltage Divider

31 Current Divider

32 esistor Network Knowing equivalent and parallel equivalents of resistors is not enough

33 Wye-Delta Transformation (1) ) ( 1 c b a c b ) ( 2 c b a a c ) ( 3 c b a b a a b c Delta -> Y Y -> Delta

34 Wye-Delta Transformation (2)

35 Practice 2.10

36 Practice 2.11

37 Practice 2.12

Kirchhoff's Laws and Circuit Analysis (EC 2)

Kirchhoff's Laws and Circuit Analysis (EC ) Circuit analysis: solving for I and V at each element Linear circuits: involve resistors, capacitors, inductors Initial analysis uses only resistors Power sources,