EEEB113 Chap 1 Notes

EEEB113

CIRCUIT ANALYSIS I

Chapter 1

Basic Concepts

1

Materials from Fundamentals of Electric Circuits, Alexander & Sadiku 4e, The McGraw-Hill Companies, Inc.

Basic Concepts - Chapter 1 2

1.1 Introduction

1.2 Systems of Units

1.3 Charge & Current

1.4 Voltage

1.5 Energy & Power

1.6 Circuit Elements

1.1 Introduction 3

What is electric circuit?

Interconnection of electrical elements.

1.2 System of Units (1)

Quantity Basic unit Symbol

1 Length meter m

2 Mass kilogram kg

3 Time second s

4 Electric current ampere A

5 Thermodynamic

temperature

kelvin K

6 Luminous intensity candela cd

4

Six basic units

International System of Units (SI), 1960

1.2 System of Units (2) 5

Common circuit theory SI prefixes

Used to signify powers of 10

e.g.

1,000,000 ohms = 1 x 106 ohms = 1 mega-ohm (M) 100,000 meters = 100 x 103 meters = 100 kilometers (km) 0.001 second = 1 x 10-3 seconds = 1 millisecond (ms) 0.0000001 farad = 0.1 x 10-6 farad = 0.1 microfarad (F)

1.2 System of Units (3) 6

Example Convert:

i) 0.01 ms to s

ii) 60 kilometers per hour to meters per second

Solution i) 0.01 ms = 1x10-2x10-3 s

= 1x10-5 s

= 1x10x10-6 s

= 10 s

ii) 60 km/hour = (60x103 m)/(60x60 s)

= 16.67 m/s

1.2 Electric Charges (1) 7

Charge, q

an electrical property, measured in coulombs (C)

Charge is bipolar

(+ve and ve charge)

Charge e on 1electron

= -1.602 10-19 C

1 coulomb of charge, 1C

= 1/(1.602 10-19 C)

= 6.24x1018 electrons

Electric current is due to flow of electronic

charge in a conductor.

Electrical effects:

Charges separate = create electric force Charges move = create electric flow i.e. current

1.2 Electric Charges (2) 8

Example Given nC, find current i at t = 0.5 s

Solution

At t = 0.5 s,

= 152.44 nA

1.3 Current (1) 9

Electric current = time rate of change of charge,

measured in ampere, A.

Charge transferred between time t0 and t is obtained

by integrating both sides of above equation.

Adt

dqi

1 A = 1C/s

t

t

idtq

0

Integrate both sides

1.3 Current (2) 10

direct current (dc)

= current remains constant with time.

alternating current (ac)

= current varies sinusoidally with time.

1.3 Current (3)

Direction of current flow Conventionally taken as positive charge movement

A current can be represented positively or negative

11

Positive ions Negative ions

(a) Positive current flow

(b) Negative current flow

11

1.3 Current (4)

Example

Calculate the amount of charge represented by four million protons.

Solution

12

1.3 Current (5)

Example

The total charge entering a terminal is given by .

Calculate the current at t = 0.5s.

Solution

13

1.3 Current (6)

Example

The current flowing through an element is

Calculate the charge entering the element from t=0 to t=2s.

Solution

14

1.4 Voltage (1)

Voltage (or potential difference) = energy required to move a unit charge through an element, measured in volts (V).

w is energy in joules (J) and q is charge in coulomb (C).

Electric voltage, vab, is always across the circuit element or

between two points in a circuit.

vab > 0 means the potential of a is higher than potential of b.

vab < 0 means the potential of a is lower than potential of b.

15

dq

dwvab

15

1.4 Voltage (2)

16

16

Point a is at higher potential than point b.

If vab= 3 V, then vba= -3 V because point b is

lower than point a.

1.5 Energy & Power (1) 17

Energy, w is the capacity to do work, measured in Joules (J);

Power, p is the rate of change of energy, measured in Watts

(W)

From the definitions of voltage and current, and

dt

dwp dtvidtpw

t

t

t

t00

vidt

dq

dq

dw

dt

dwp

1.5 Energy & Power (2)

Passive sign convention is satisfied:

1. When the current enters through the positive terminal of an element, the power is delivered to or absorbed by the element, p=+vi.

2. When the current enters through the negative terminal, the power is delivered from or supplied by the element, p=-vi.

18

i

+

v

p = +Vi absorb power

i

+

v p = -Vi supply power


In a circuit,

+ power absorbed = - power supplied

Law of conservation of energy

Algebraic SUM of POWER in a circuit at any instant of time is ZERO

0p

19


20

20

Example

Find the power delivered to the element at t = 5ms if the current remains the same but the voltage is:

Solution


21

21

Solution cont.


22

22

Example

A stove draws 15 A when connected to a 240-V line. How long does it take to consume 60kJ?

Solution

1.6 Circuit Element (1) 23

2 types of electrical/ circuit elements

Passive elements

1. Resistor

2. Capacitor

3. Inductor

Passive

Active able to generate

energy

e.g. sources,

batteries,

generators

cannot generate

energy


Active elements

Sources

1. Independent voltage source

2. Independent current source

3. Dependent sources

Voltage

Current

active element that provides

voltage or current that is

independent of other circuit elements.

active element that depends on

voltage or current of other element.

+ -

+ -

Independent: Dependent:

Voltage Current Voltage Current


Independent sources:

voltage sources current source


4 types of Dependent Sources

1. Voltage-controlled voltage source (VCVS)

2. Current-controlled voltage source (CCVS)

3. Voltage-controlled current source (VCCS)

4. Current-controlled current source (CCCS)

2V0 + -

2I0 + -

2I

2V0

1.6 Circuit Elements (5) 27

Active Elements Passive Elements

Independent sources

Dependant sources

A dependent source is an active element in which the source quantity is controlled by another voltage or current.

They have four different types: VCVS,

CCVS, VCCS, CCCS. Keep in minds the signs of dependent sources.

1.6 Circuit Elements (6) 28

Example

Find the power absorbed or supplied by each component of the circuit

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EEEB113 Chap 1 Notes