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1. Chapter 1
Fundamentals of Electric Circuits
Circuit is a current path, it is needed for
some electrical equipment by certain
Or elements combined in a certain way up.

2. Circuit R, I, U, C, L, etc.
Current I
Voltage V
Charge Q=I*t
Resistance resistor R
Capacitance capacitor C
Inductance inductor L

3. Learning Objectives:
1. Identify the principal elements of electric circuits:
nodes, loops, meshes, branches, voltage and
current sources;
2. Apply Kirchhoff’s laws to simple electric circuits
and derive the basic circuit equations.
3. Compute the power delivered or absorbed by
circuit elements.
4. Apply the voltage and current divider laws to
calculate unknown variables in simple series,
parallel, and series-parallel circuits.

4. The voltage independent source
The current independent source
The ideal voltage source:
Independent Sources
I
b
E
V
R0
RL
+
_
+
_
a
V = E – R0 I
V0 = E
Is =
O I/A
V/V
R0
E
E RL
I
b
V
+
_
+
_
a
When R0 = 0, V = E, the source is
called ideal voltage source.
R0 = 0

5. V0 = IS R0
IS
O I/A
V/V R0 = 
R0
V
IS = + I
When R0 =  , I = IS, the
source is called ideal current
source.
R0
I
V RL
+
–
IS
R0
V
The ideal current source:

6. current
controlled voltage
source
Voltage
controlled current
source
current
controlled current
source
(CCVS)
(VCCS)
(CCCS)
Voltage
controlled voltage
source
(VCVS)
Dependent (Controlled) Sources

7. Voltage
divider
Equivalent series
resistance
R
i
+
–
§1-4 Series resistors and voltage divider rule
1 2
eq
R R R
 

 1

1
R
i


 2
R


2
 
2
1
1
2
1
1
1
1
R
R
R
R
R
R
i
R








2
1
2
2
1
2
2
2
R
R
R
R
R
R
i
R









8. Current
divider
Equivalent parallel
resistance
R
i
+
–
§1-5 Parallel resistors and current divider rule
1 2
1 2
eq
R R
R
R R



1
R
i


 2
R
1
i 2
i
i
R
R
R
R
R
R
R
R
i
R
i
2
1
2
1
2
1
2
1
1
1






i
R
R
R
i
2
1
1
2



9. Current
divider
Equivalent parallel
resistance 1 2
1 1 1 1
...
eq N
R R R R
   
R
i
+
–

1
1
1 2
1
1 1 ... 1 N
R
i i
R R R

  
1
R
i


 N
R
1
i N
i
2
i
…
1 2
1
1 1 ... 1
N
N
N
R
i i
R R R

  

10. §1-6 Source transformations
The ideal voltage source and a series resistance comprise a
practical voltage source. internal resistace of
the voltage source
s
R  
L
s
s
L
R
R
i




L
s
L
s
L
L
L
R
R
R
i
R






A practical current source is defined as an ideal current
source in parallel with an internal resistance Rsi.
s
L
si
L
si
L i
R
R
R
R



s
L
si
si
L
L
L i
R
R
R
R
i


 /

L
R
L
i


L



s

Rsv
L
R
L
i


L

s
i
Rsi
internal resistace of
the current source
si
R  

11. We shall define two sources as being equivalent if
each produces identical current and identical voltage
in any loads which is placed across its terminals.
Conditions of equivalence:
L
s
s
L
R
R
i




s
L
si
si
i
R
R
R


s
si
s R
R
R 

  s
s
s i
R


L
R
L
i


L



s

Rsv
L
R
L
i


L

s
i
Rsi

12. s
si
s R
R
R 

 
Example:
A
iL 1
)
4
2
2
(
3 


1 4 4
L V
   
A
iL 1
4
2
6



1 4 4
L V
   


V
6
2 L
i


L
 4
2
L
i


L
 4
A
3
s
s
s i
R


L
s
s
L
R
R
i




s
L
si
si
i
R
R
R


4
3
4
4 3 12
L L
A L s
P i W
P i W


  
   
4
6
4
6 1 6
L L
V s L
P i W
P i W


  
   