# on video The general laws of electricity

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

−

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