ELECTRIC CIRCUIT NOTE CHAPTER 2.pdf | Series And Parallel ...

ECE 1311: Electric Circuits Chapter 2: Basic laws

Basic Law Overview 

Ideal sources –  sources –  series  series and parallel

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Ohm’s law

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Definitions –  Definitions –  open  open circuits, short circuits, conductance, nodes, branches, loops

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Kirchhoff's law

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Voltage divider and series ser ies resistors resistor s

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Current divider and parallel resistors

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Wye-Delta transformations

Ideal Voltage Source 

Ideal voltage source in series can be added

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Ideal voltage source in parallel = NO GOOD

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Recall: ideal voltage source guarantee the voltage between two two terminals ter minals is at the specified potential (voltage) (voltage)

BOOM

Ideal Current Source 

Ideal current source cannot be connected in series

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Ideal current current source in parallel can be added

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Recall: ideal current guarantee the current cur rent flowing through source is at the specified value

Recall: Current entering a circuit must be equal to the current leaving the circuit

BOOM

Resistance 

All material resist the flow of current given by R • R = resistance of an element in ohms

 R 

 l 

 A

• p = resistivity of material in ohm-meters • l = length of material in meters • A = cross sectional area of material in meter2

Ohm’s Law (1) 

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Ohm ’s law states that the voltage across a resistor is directly Ohm’ proportional to the current flowing through the resistor.

v  iR Only material with linear relationship satisfy Ohm’s law (note the PSC)

Ohm’s Law (2) 

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Two extreme possible possi ble values of R: 0 (zero) and (infinite) (infi nite) are related with two basic circuit concepts: short circuit and open circuit.. circuit Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens. 1 i G   R v The power power dissipated by a resistor:

 p  v i  i 2 R  

v2  R

Power absorbed by R is always positive

Practice 2.1

Shortt circuit Shor 

An element (or wire) with R = 0 is called a short circuit

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An ideal voltage source with V = 0 is equivalent to a short circuit

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Since v = iR i R and R = 0, v = 0 regardless of i

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Recall: cannot connect voltage source to a short circuit

Open circuit 

An element with R =

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Often represented by a wire with an open connection

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is called the open circuit

An ideal current source I = 0A is also equivalent e quivalent to an open circuit

Recall: cannot connect current source to an open circuit

Formalization 

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

Nodes, Branches and Loops 

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A branch  branch represents  represents a single element such as a voltage source or a resistor. A node is the point of connection between between two or more  branches.

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A loop loop is  is any closed path in a circuit.

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A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:

b  l   n  1

Practice 2.2

How many branches, nodes and independent loops are there?

Practice 2.3

How many branches, nodes and loops are there?

Overview on Kirchhoff’s La L aw 

It’s the foundation of circuit analysis

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There are two - Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL)

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It tell us how the voltage and current are related within a circuit element are related

Kirchhoff’s Current Law (1) 

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

Kirchhoff’s Current Law (2) 

KCL also apply at the boundary

Practice 2.4 

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

Kirchhoff’s Voltage Law (1) 

Kirchhoff’ Kirchhoff ’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.

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Based on the conservation conser vation of energy

Practice 2.5

Practice 2.6 Apply KVL to find the value I

Summary on Ohm’s Law, KCL and KVL 

Ohm’s Law

v  iR

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KCL

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KVL

 I  V 

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These law alone are sufficient to analyze many circuits

n

0

n

0

Practice 2.7 

Find v2, v6 and vI

Practice 2.8 Find i0 and v0

Practice 2.9

Resistor Circuit Overview 

Resistors in series

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Resistors in parallel

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Voltage dividers

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Current dividers

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Wye-Delta transformation

Resistors Resist ors in series

Resistors Resist ors in Parallel (1)

Resistors Resist ors in Parallel (2)

Voltage Divider

Current Divider

Resistor Network 

Knowing equivalent equivalent and parallel equivalents of resistors resistor s is not enough

Wye-Delta Transformation (1)

Delta -> Y

 R1



 R2



 R3

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Y -> Delta

 Rb Rc ( Ra

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 Rb

 Ra

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 Rb

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 Rc )

 Ra Rb ( Ra

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 Rb

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 Rc )

 Rb

 Rc





 R2 R3

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 R3 R1

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 R3 R1

 R1

 Rc )

 Rc Ra ( Ra



 R1 R2

 R1 R2

 R1 R2

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 R2 R3  R2

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 R2 R3  R3

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 R3 R1

Wye-Delta Transformation (2)

Practice 2.10

Practice Practi ce 2. 2.11 11

Practice 2.12