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
v  dw
dq
Volt (joule/coulumb)
where
v = the voltage in volts
w = the energy in joules
q = the charge in coulombs
The rate of flow of charges is called the current which is expressed as
i  dq
dt
Ampere (coulumb/second)
where
i = the current in amperes
q = the charge in coulombs
t = the time in seconds
The voltage and current definition:
v  dw
dq
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 )‫ (مثالي‬basic circuit element be as follows:
i
+
v
-
Blank box ( or black box)
1
2
We use the word ideal )‫ (مثالي‬to 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
i
Example
We are going to discuss later ideal elements and
non ideal elements
+
v
-
Resistor
We are using black box because we are making
no commitment at this time as the type of circuit
elements
The polarity reference for the voltage is indicated by the + and - signs
The reference direction of the current is shown by the arrow
i
+
v
-
1
2
The interpretation of these references is as follows, let the voltage difference between
terminal 1 and 2 is 3 V
+
3V
-
1
( v1)
2
( 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
+
3V
-
1
( v1)
2
( v2)
Note : the polarity shown doesn't mean that V1 is positive or V2 is negative ,
what that is imply is
V1
Example
v
= 10
1
v
1
= - 10
v
v
1
= 3
1
= 0
-
V2 = + 3 V




v
v
v
v
=
7
2
=
- 13
2
=
0
2
=
-3
2
The reference direction of the current is shown by the arrow
i
+
v
-
1
2
The interpretation of these references is as follows
i=3A
Positive charges flowing
from terminal 1 to terminal 2
OR
Negative charges flowing
from terminal 2 to terminal 1
+++++++
+
++++++
1
2
i=3A
------------
1
2
i = -3 A
Positive charges flowing
from terminal 2 to terminal 1
OR
Negative charges flowing
from terminal 1 to terminal 2
+++++++
+
++++++
1
2
i = -3 A
------------
1
2
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
+
v
-
1
The polarity of the voltage and the current
direction shown is called
passive sign convention
2
The interpretation of these references is as follows
Positive Values
v
or
i
Negative Values
voltage drop from 1 to 2
v
voltage rise from 1 to 2
voltage rise from 2 to 1
or
voltage drop from 2 to 1
positive charge flowing from 1 to 2
i
positive charge flowing from 2 to 1
or negative charge flowing from 2 to 1 or negative charge flowing from 1 to 2
1.6 Power and Energy
Power is defined as the time rate of expanding or absorbing energy
P  dw
dt
where
1 W1 J
1s
W
P - power in Wattts
w - Energy in Joules
t - Time in Seconds
P  dw =  dw
 dq
dt





 dq

 dt





 vi
This show that the power is simply the product of the current in the element and the
voltage across the element
Since power is dependent on the polarity of voltage and direction of current
i
+
v
-
1
2
Therefore,
power is positive (absorbed)
or power is negative (delivered)
i
i
+
v
-
1
2
i
v
+
+
v
-
1
2
P  vi
P  - vi
i
1
2
P  -vi
v
+
1
2
P  vi
Example1: Suppose we have the following voltage and current :
i=4A
+
1
-10
-
2
Q: What is the power
P
and determine if it is absorbed or delivered
A: since P is given as
P  - vi  - (-10)(4)  40 W  power is absorbed
Example2: Consider the following circuit
The power absorbed by the 10 V battery
is
 - (10)(5)  - 50 W
P
 The batterey is delivering 50 W
10V
The power absorbed by the 2 W resistor is
P  (10)(5)
2W
Note :
 50 W
|P |= |P |
10V
2W
 The resistor is absorbing 50 W
 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 - 40 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,
P
vi  (-40)(12)  -480 W  Batterey of car A is delivering power
car A
 Batterey of car B is absorbing power  Car B must have the dead battery