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Introduction :
A dipole is a receiver or generator of electrical energy, capable of converting electrical energy into a different type of energy (chemical, thermal, etc.)
dipole definition
(a): Generator convention: the current and voltage arrows are in the same direction.
(b): Receiver convention: the current and voltage arrows are in opposite directions.
II. Ideal voltage source:
A supposedly ideal DC generator (source) is a generator which supplies, between its terminals, a constant potential difference, whatever the intensity of the current which crosses it, provided that the load is not zero.
We also call the ideal voltage source, an electromotive force U denoted by the abbreviation “f.e.m”
voltage source
Different symbols for a voltage source
Example :
voltage source
III. Ideal current source:
A generator (source) of direct current supposed to be ideal is a generator fixing the intensity of the electric current Ig which crosses it whatever the potential difference U at these terminals, provided that the load is not infinite.

Different symbols for a current source
Example :
Power source
IV. Ohm's Law:
In continuous operation, in an electrical circuit, Ohm's law is stated: a resistor R through which a current I flows develops a potential difference across its terminals given by:
ohm's law
U
HAS
B
=
V
HAS
V
B
=
R
×
I

U

e
not

V
oh
I
you

I

e
not

HAS
m
p
e
r
e
R

e
not

O
h
m
We generalize Ohm's law for alternating current: a dipole of impedance Z, traversed by an alternating current i(t) whose complex representation is I develops a potential difference u(t) whose complex representation is U given by:
Z: complex impedance made up of linear dipoles (resistors, capacitances and inductances)

V. Kirchhoff's laws:
1. Law of stitches:
The algebraic sum of the voltages counted in a given direction is zero.
In the circuit opposite, there are 3 links:
law of stitches
- In mesh 1 (ABFG):
E – UAB + UFB – UFG = 0
- In mesh 2 (BCDEF):
UFB + UEF + UDE + UCD + UBC = 0
- In mesh 3 (ABCDEFG):
E – UAB – UBC – UCD – UDE – UEF – UFG = 0
Example :
Calculate UAB , Deduce UBA.

The mesh law will give us:
10V – 5V – UAB + (-3V) = 0 hence UAB = 10 – 5 – 3 = 2V
And we have UBA = VB – VA = – (VA – VB) = – 2V
2. Law of knots:
The sum of currents entering the node equals the sum of currents leaving.
Law of knots
Then: I1 + I2 = I3 + I4 + I5
Example:
Calculate current I1:
Law of knots
According to the law of nodes we have: I1 + 2A = 1.5A → I1 = -0.5 A
VI. Association of dipoles:
1. Series association of two dipoles:
The mesh law will give us: U = V1 + V2
association of resistance
According to Ohm's law we can write:
U

=

R
1
I

+

R
2
I

U

=

(
R
1
+

R
2
)
I

U

=

R
e
q
I

HAS
v
e
vs
:

R
e
q
=

R
1
+

R
2
2. Parallel association of two dipoles:
The knot law will give us: i = i1 + i2
association of resistance
However, according to the mesh law, we have:
I
=
U
R
1
+
U
R
2

I
=
(
1
R
1
+
1
R
2
)
U
So :
U
=
1
1
R
1
+
1
R
2
I
=
R
1
R
2
R
1
+
R
2
I
=
R
e
q
I
With
R
e
q
=
R
1
R
2
R
1
+
R
2
VII. Dividing bridges:
1. Voltage divider:
divider bridge
The voltage V1 is written:
V
1
=
R
1
R
1
+
R
2
V
0
The voltage V2 is written:

V
2
=
R
2
R
1
+
R
2
V
0
2. Current divider:
divider bridge
The voltage i1 is written:
I
1
=
R
2
R
1
+
R
2
I
0
The voltage i2 is written:
I
1
=
R
2
R
1
+
R
2
I
0
VIII. Millman's theorem:
This theorem gives the potential of a point of the circuit is translated by:
Millman's theorem

Introduction :
A dipole is a receiver or generator of electrical energy, capable of converting electrical energy into a different type of energy (chemical, thermal, etc.)
dipole definition
(a): Generator convention: the current and voltage arrows are in the same direction.
(b): Receiver convention: the current and voltage arrows are in opposite directions.
II. Ideal voltage source:
A supposedly ideal DC generator (source) is a generator which supplies, between its terminals, a constant potential difference, whatever the intensity of the current which crosses it, provided that the load is not zero.
We also call the ideal voltage source, an electromotive force U denoted by the abbreviation “f.e.m”
voltage source
Different symbols for a voltage source
Example :
voltage source
III. Ideal current source:
A generator (source) of direct current supposed to be ideal is a generator fixing the intensity of the electric current Ig which crosses it whatever the potential difference U at these terminals, provided that the load is not infinite.

Different symbols for a current source
Example :
Power source
IV. Ohm's Law:
In continuous operation, in an electrical circuit, Ohm's law is stated: a resistor R through which a current I flows develops a potential difference across its terminals given by:
ohm's law
U
HAS
B
=
V
HAS
V
B
=
R
×
I

U

e
not

V
oh
I
you

I

e
not

HAS
m
p
e
r
e
R

e
not

O
h
m
We generalize Ohm's law for alternating current: a dipole of impedance Z, traversed by an alternating current i(t) whose complex representation is I develops a potential difference u(t) whose complex representation is U given by:
Z: complex impedance made up of linear dipoles (resistors, capacitances and inductances)

V. Kirchhoff's laws:
1. Law of stitches:
The algebraic sum of the voltages counted in a given direction is zero.
In the circuit opposite, there are 3 links:
law of stitches
- In mesh 1 (ABFG):
E – UAB + UFB – UFG = 0
- In mesh 2 (BCDEF):
UFB + UEF + UDE + UCD + UBC = 0
- In mesh 3 (ABCDEFG):
E – UAB – UBC – UCD – UDE – UEF – UFG = 0
Example :
Calculate UAB , Deduce UBA.

The mesh law will give us:
10V – 5V – UAB + (-3V) = 0 hence UAB = 10 – 5 – 3 = 2V
And we have UBA = VB – VA = – (VA – VB) = – 2V
2. Law of knots:
The sum of currents entering the node equals the sum of currents leaving.
Law of knots
Then: I1 + I2 = I3 + I4 + I5
Example:
Calculate current I1:
Law of knots
According to the law of nodes we have: I1 + 2A = 1.5A → I1 = -0.5 A
VI. Association of dipoles:
1. Series association of two dipoles:
The mesh law will give us: U = V1 + V2
association of resistance
According to Ohm's law we can write:
U

=

R
1
I

+

R
2
I

U

=

(
R
1
+

R
2
)
I

U

=

R
e
q
I

HAS
v
e
vs
:

R
e
q
=

R
1
+

R
2
2. Parallel association of two dipoles:
The knot law will give us: i = i1 + i2
association of resistance
However, according to the mesh law, we have:
I
=
U
R
1
+
U
R
2

I
=
(
1
R
1
+
1
R
2
)
U
So :
U
=
1
1
R
1
+
1
R
2
I
=
R
1
R
2
R
1
+
R
2
I
=
R
e
q
I
With
R
e
q
=
R
1
R
2
R
1
+
R
2
VII. Dividing bridges:
1. Voltage divider:
divider bridge
The voltage V1 is written:
V
1
=
R
1
R
1
+
R
2
V
0
The voltage V2 is written:

V
2
=
R
2
R
1
+
R
2
V
0
2. Current divider:
divider bridge
The voltage i1 is written:
I
1
=
R
2
R
1
+
R
2
I
0
The voltage i2 is written:
I
1
=
R
2
R
1
+
R
2
I
0
VIII. Millman's theorem:
This theorem gives the potential of a point of the circuit is translated by:
Millman's theorem