+ - + - + - + - + - + - + - + - + - + - + -+ - + - + - + - + - + - + - + - + -

+ ++ ++ ++ ++ +++++ ++ ++ ++ ++ +++++ ++ ++ ++ ++ ++++

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Unseparated charges

separated charges

Work or Energy must be done to separate positive and negative charges

Voltage is the energy per unit charge created by the separation, which can be expressed as

joule/coulumb( )Voltdwvdq

where = the voltage in volts = the energy in joules = the charge in coulombs

vwq

The rate of flow of charges is called the current which is expressed as

coul( )umb/secondAm peredqidt

where = the current in amperes = the charge in coulombs = the time in seconds

iqt

The voltage and current definition:

dqdwv i

dq dt

are definitions for the magnitude of voltage and current

The bipolar nature of electric charge ( + , - ) require that we assign polarity references to these variables ( voltage and current) as will be done next section

Although current is made up of discrete moving electrons, we consider them and their charges as smoothly continues due to the enormous numbers

Circuit model tell us the relation between the voltage and current

Two different physically different components could have the same relationship between the voltage and current.

If they do, for the purpose of circuit analysis they are identical

The Ideal Basic Circuit Element

Let an ideal (مثالي) basic circuit element be as follows:

+

-

1

2v

i

We use the word ideal (مثالي) to imply that a basic circuit element does not exist as a realizable physical component

We use the word basic to imply that the circuit element cannot be further reduced or subdivided into other elements

Blank box ( or black box)

Example

Resistor

i

v

+

-

We are going to discuss later ideal elements and non ideal elements

We are using black box because we are making no commitment at this time as the type of circuit elements

+

-

1

2v

i

The polarity reference for the voltage is indicated by the + and - signs

The interpretation of these references is as follows, let the voltage difference between terminal 1 and 2 is 3 V

The reference direction of the current is shown by the arrow

+

-

1 ( v1)

3 V2 ( v2)

V1 > V2 by 3 V voltage drop from terminal 1 to terminal 2 by 3 V or voltage rise from terminal 2 to terminal 1 by 3 V

V2 < V1 by 3 V OR V2 > V1 by -3 V

+

-

1 ( v1)

3 V2 ( v2)

Note : the polarity shown doesn't mean that V1 is positive or V2 is negative , what that is imply is

V1 - V2 = + 3 V

Example

1 2 v v = 10 = 7

1 2 v v - -= 10 = 13

1 2 v v = 3 = 0

1 2 v v -= 0 = 3

+

-

1

2v

i

The interpretation of these references is as follows

1

2

The reference direction of the current is shown by the arrow

i = 3 A

+ + + + + + ++

+ + + + + +Positive charges flowing

from terminal 1 to terminal 2

1

2

i = 3 A

- - - - - - --

- - - - - - Negative charges flowing

from terminal 2 to terminal 1

OR

1

2

i = -3 A

+ + + + + + ++

+ + + + + +Positive charges flowing

from terminal 2 to terminal 1

1

2

i = -3 A

- - - - - - --

- - - - - - Negative charges flowing

from terminal 1 to terminal 2

OR

+

-

1

2v

i

Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element, use a positive sign in any expression that relates the voltage to the current

The interpretation of these references is as follows

Positive ValuesNegative Values

v voltage drop from 1 to 2

or voltage rise from 2 to 1

v voltage rise from 1 to 2

or voltage drop from 2 to 1

i positive charge flowing from 1 to 2

or negative charge flowing from 2 to 1

i positive charge flowing from 2 to 1

or negative charge flowing from 1 to 2

The polarity of the voltage and the current direction shown is called

passive sign convention

1.6 Power and Energy

Power is defined as the time rate of expanding or absorbing energy

W dwPdt

where power in Wattts Energy in Joules Time in Seconds

Pwt

---

1 J 1

1 Ws

dwPdt

This show that the power is simply the product of the current in the element and the voltage across the element

= dqdwdq dt

vi

+

-

1

2v

i

Therefore, power is positive (absorbed)

or power is negative (delivered)

Since power is dependent on the polarity of voltage and direction of current

+

-

1

2v

i

P vi

+

-

1

2v

P vi-

i

-

+

1

2v

i

P vi -

-

+

1

2v

P vi

i

+

-

1

2-10

i = 4 A

Example1: Suppose we have the following voltage and current:

P vi-

Q: What is the power P and determine if it is absorbed or delivered

A: since P is given as

( 10)(4) - - 40 W power is absorbed

Example2: Consider the following circuit

The power absorbed by the 10 V battery is

50 W -10

(10)(5) V

P - The batterey is delivering 50 W

The power absorbed by the resistor is

50 W (10)(5) P The resistor is absorbing 50 W

Note : 10 = | | | |VP P Power deliver = Power absorbed

Example3: Consider the following car battery connection. One battery is dead and the other one is charging it. If the current i is measured and found to be - A , which car had the dead battery

Since the current i is in the direction of the voltage drop across the 12 V battery ( the current i flows into the + terminal of the battery of car A)

Therefore using the passive sign convention ,

car AP vi ( 40)(12) - 480 W- Batterey of car A is delivering power

Batterey of car B is absorbing power Car B must have the dead battery