Unit 3: Direct current and electric resistance Electric current - - PowerPoint PPT Presentation

Unit 3: Direct current and electric resistance

• Electric

current and movement

• f

charges. Intensity of current and drift speed.

• Density of current in homogeneous currents.
• Ohm’s

law. Resistance

• f

a homogeneous conductor of constant cross section.

• Changes in resistivity depend on temperature
• Resistors association.

Series and parallel association.

Tipler, chapter 25, part 25.1

t q I ∆ ∆ =

Electric current and movement of charges

• An electric current occurs when a conductor is not in

electrostatic equilibrium. This can be achieved by applying an electric field ≠ 0 to the conductor. Intensity is a base quantity. Unit: Ampère I is the same for any cross section of the conductor

E

+ + + +

• Although the moving particles in a conductor are electrons,

for historical reasons electric current is studied as positive charges moving in the direction of the electric field.

Electric current and movement of charges

• The

charges collide with the nuclei of the atoms, causing chaotic movement.

• These collisions set up a

resistance to the movement of the charges (electric resistance).

• An average speed (drift speed Vd) can be

computed for the charges, Vd being related to E. This rate is called mobility (µ):

Vd

E vd = µ

Drift speed is the modulus of vector drift velocity

d d

A q n t t A q n t q I v v = ∆ ∆ = ∆ ∆ =

Electric current and movement of charges

A characteristic of each conductor is the number of free electrons per unit of volume (n) (density of charge carriers), which depends on the chemical structure of the material. Our hipothesys is that all the electrons are moving at once (like a log) inside the conductor. Obviously, I and Vd are related through n:

Vdt: distance covered by an electron during Δt A: cross section of conductor AVdt: volume crossing A during Δt nqAVdt: charge crossing A during Δt

• Current density (J) is the intensity of current

through a cross section of the conductor, divided into the section. This rate can be computed at any point of the cross section: Density of electric current in homogeneous conductors.

d d

nqv A nqAv A I J = = =

[J]=IL-2

I

• is a vector with the same direction as

at any point:

J

• E
• E

J

• σ

=

Omh’s Law

J

• E

σ conductivity ≅ (Ωm)-1

Materials obeying Ohm’s law are called ohmic materials.

Tipler, chapter 25, part 25.2

Ohm’s Law ρ=1/σ resistivity ≅ Ωm Ω-1 = S (Siemens)

a b

V V L R R I A ρ − = = =

Electric Resistance of a homogeneous conductor of constant cross section.

A L I dr A I dr A I dr J Edr r d E V V

b a b a b a b a

ρ σ σ σ

b a b a

= = = = = = −

    

• Tipler, chapter 25, part 25.2

E is always pointing to lower potentials (Va>Vb) R is called electrical resistance of conductor, depending

• n

its material, shape and size. Is measured in Ohms

[R]=ML2T-1Q-2

Changes in resistivity depending on temperature

Tipler, chapter 25, section 25.2

• The resistance of conductors increases with temperature due

to the higher number of collisions between free electrons and nuclei.

[ ]

C T º ( 20 1

20

− + = α ρ ρ

Combinations of resistors. Resistors in series.



=

=

n i i eq

R R

1

Tipler, chapter 25, section 25.4

1 2 1 2

( )

a c

V V IR IR I R R − = + = +

a c eq

V V IR − =

1 2 eq

R R R = +



=

=

n i i eq

R R

1

1 1

Combinations of resistors. Resistors in parallel.

1 2 1 2 1 2

1 1 ( )( )

a b a b a b

V V V V I I I V V R R R R − − = + = + = − +

a b eq

V V I R − =

1 2

1 1 1

eq

R R R = +