Chapter 2 Basic Law

7/30/2019 Chapter 2 Basic Law

1/46

1

Basic Laws of ElectricCircuit

Zuraida Hanim Binti Zaini


2/46

2

Basic Laws Overview Ideal sources: series & parallel

Resistance & Ohms Law

Definitions: open circuit, short circuit & conductance

Definitions: nodes, branches & loops Kirchhoffs Law

Voltage dividers & series resistors

Current dividers & parallel resistors

Wye-delta Transformations


3/46

3

Ideal Voltage Sources: Series

Ideal voltage sources connected in series add


4/46

4

Ideal Voltage Sources: Parallel

Ideal voltage sources cannotbe connected in parallel

Recall: ideal voltage sources guarantee the voltage between twoterminals is at the specified potential (voltage)

Immovable object meets unstoppable force

In practice, the stronger source would win Could easily cause component failure (smoke)

Ideal sources do not exist

Technically allowed ifV1 = V2, but a bad idea


5/46


6/46

6

Ideal Current Sources: Parallel

Ideal current sources in parallel add


7/46

7

Resistance

All materials resist the flow of current

Resistance is usually represented by the variableR

Depends on geometry and resistivity of the material


8/46

8

Ohms Law

As with all circuit elements, we need to know how the current throughand voltage across the device are related

Many materials have a complicated nonlinear relationship (including

light bulbs): v = f (i) Materials with a linearrelationship satisfy Ohms law: v = mi

The slope, m, is equal to the resistance of the element

Ohms Law: v = iR

Sign, , is determined by the passive sign convention (PSC)


9/46

9

Resistors & Passive Sign Convention

Recall that relationships between current and voltage are signsensitive

Passive Sign Convention: Current enters the positive terminals of an

element If PSC satisfied: v = iR

If PSC not satisfied: v = iR


10/46

10

Other Equations Derived from Ohms Law

Ohms law implies:

Recallp = vi. Therefore

Resistors cannot produce power Therefore, the power absorbed by a resistor will always be positive

1 = 1 V/A


11/46

11

Example 1: Ohms Law


12/46


13/46

13

Short Circuit as Voltage Source (0 V)

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

Since v = iR andR = 0, v = 0 regardless ofi

Could draw a source with Vs = 0 V, but is not done in practice

Cannot connect a voltage source to a short circuit Irresistible force meets immovable object

In practice, the wire usually wins and the voltage source melts (if notprotected)


14/46

14

Open Circuit

An element withR = is called a open circuit

Often just omitted

Could draw a resistor withR = , but is unnecessary and would add

clutter


15/46

15

Open Circuit as Current Source (0 A)

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

Could draw a source with I = 0 A, but is not done in practice

Cannot connect a current source to an open circuit

Irresistible force meets immovable object In practice, you blow the current source (if not protected)

The insulator (air) usually wins. Else, sparks fly


16/46

ECE 1131 Electric Circuits

Semester II 2008-2009

16

Conductance

Sometimes conductance is specified instead of resistance

Conductance is a measure of the ability of an element to conductelectric current

Inverse of resistance


17/46

17

Circuit Building Blocks

Before we can begin analysis, we need a common language ad

framework fro describing circuits

For this course, networks and circuits are the same

Networks are composed of nodes, branches and loops


18/46

18

Nodes Defined

Example: How many nodes? How many essential nodes?

Node: the point of connection between two or more branches

May include a portion of the circuit (more than a single point) Essential Node: the point of connection between three or more

branches


19/46

19

Branches Defined

Example: How many branches?

Branch: a single two-terminal element in a circuit

Segments of wire are not counted as elements (or branches) Examples: voltage source, resistor, current source


20/46


21/46


22/46

22

Kirchhoffs Current Law

Kirchhoffs Current Law (KCL): the algebraic sum of currentsentering a node (or a closed boundary) is zero

The sum of currents entering a node is equal to the sum of the currentsleaving a node

Common sense:

All of the electrons have to go somewhere

The current that goes in, has to come out some place

Based on law of conservation of charge


23/46

23

Kirchhoffs Current Law for Boundaries

KCL also applies to closed boundaries forallcircuits


24/46

24

Example 2: Kirchhoffs Current Law


25/46

25

Kirchhoffs Voltage Law

Kirchhoffs Voltage Law (KVL): the algebraic sum of voltages

around a closed path (or loop) is zero

Based on the conservation of energy

Analogous idea in hydraulic systems: sum of pressure drops and rises

in any closed path must be equal


26/46


27/46

27

Comments on Ohms Law, KCL and KVL

Much of the circuit analysis that we will do is based on these three laws

These laws alone are sufficient to analyze many circuits


28/46


29/46

29

Example 5: Applying the Basic Laws


30/46

30

Example 6: Applying the Basic Laws


31/46

31

Resistive Circuits Overview

Resistors in series

Resistors in parallel

Voltage dividers

Current dividers Wye-Delta transformations


32/46

32

Resistors in Series

Resistors in series add

Similar to voltage sources

Electrically, there is no difference between the two circuits


33/46

33

Resistors in Parallel


34/46

34

Resistors in Parallel

Resistors in parallel have a more complicated relationship

Easier to express in terms of conductance

For two resistors:


35/46

35

Voltage Divider


36/46

36

Current Divider


37/46

Example: More than one source

Find I1 and I2

Is1 Is2 VR1 R2

+

I1 I2


38/46

Example: More than one source (Cont.)

Apply KCL at the top node

2121

2121

11

RR

V

R

V

R

VIIII

ss

Is1 Is2 VR1 R2

+

I1 I2

21

21

21

RR

RRIIVss


39/46

ECE 1131 Electric Circuits

Semester II 2008-2009

39

Exercise 2.13


40/46

40

Exercise 2.36 (Current Division)


41/46


42/46

42

Example 1: Resistor Networks


43/46

43

Resistor Networks: Comments

Knowing the equivalent and parallel equivalents of resistors is not

quite adequate

There are some configurations that require one more tool


44/46


45/46

45

Delta Wye Transformations


46/46

Example 2:

Delta Wye Transformation

Chapter 2 Basic Law

Documents