1. 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

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

3. The voltage and current definition:
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

4. The Ideal Basic Circuit Element
Let an ideal (مثالي) basic circuit element be as follows: i
Blank box ( or black box) + 1 v - 2
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
Example
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

5. The polarity reference for the voltage is indicated by the + and - signs
The reference direction of the current is shown by the arrow i + 1 v - 2
The interpretation of these references is as follows, let the voltage difference between terminal 1 and 2 is 3 V +
1 ( v1)
3 V -
2 ( v2)
V1 > V 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

6. +
1 ( v1)
3 V -
2 ( v2)
Note : the polarity shown doesn't mean that V1 is positive or V2 is negative , what that is imply is
V V2 = + 3 V
Example

7. i + v - i = 3 A i = 3 A + + + + + + + + + + + + + + - - - - - - - -
The reference direction of the current is shown by the arrow i + 1 v - 2
The interpretation of these references is as follows
i = 3 A 1 +
Positive charges flowing
from terminal 1 to terminal 2 2
i = 3 A OR 1 -
Negative charges flowing
from terminal 2 to terminal 1 2

8. i = -3 A i = -3 A + + + + + + + + + + + + + + - - - - - - - -1 +
Positive charges flowing
from terminal 2 to terminal 1 2
i = -3 A OR 1 -
Negative charges flowing
from terminal 1 to terminal 2 2

9. i positive charge flowing from 2 to 1
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 i
The polarity of the voltage and the current direction shown is called
passive sign convention + 1 v - 2
The interpretation of these references is as follows
Negative Values
Positive Values
v voltage rise from 1 to 2
or voltage drop from 2 to 1
v voltage drop from 1 to 2
or voltage rise from 2 to 1
i positive charge flowing from 2 to 1
or negative charge flowing from 1 to 2
i positive charge flowing from 1 to 2
or negative charge flowing from 2 to 1

10. 1.6 Power and Energy
Power is defined as the time rate of expanding or absorbing energy
This show that the power is simply the product of the current in the element and the voltage across the element

11. i + v - i i + + v v - - i i - - v v + +
Since power is dependent on the polarity of voltage and direction of current i + 1
Therefore,
power is positive (absorbed)
or power is negative (delivered) v - 2 i i + 1 + 1 v v - 2 - 2 i i - 1 - 1 v v + 2 + 2

12. Example1: Suppose we have the following voltage and current :
i = 4 A + 1
-10 - 2
Q: What is the power P and determine if it is absorbed or delivered
A: since P is given as

13. Example2: Consider the following circuit
The power absorbed by the 10 V battery is
The power absorbed by the 2 W resistor is
Note :

14. Example3: Consider the following car battery connection
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,