Electrostatics Electric circuits

Ohm’s Law

lecturer: Kristóf KarádiOriginal slide:Kata Türmer (changes: Kristóf Karádi)

11.03.2019.

Electric Charge

Ancient Greeks

◦amber: elecktron [gr]

◦(magnetite).

Law of charges:

Same charges repel, and different charges attract.!

+ +

+ + +

+ + -

-

-

-

-

--

Benjamin Franklin (1706-1790): the charge left on a glass rod after rubbing with rabbit fur was given the name “positive”, while that left on amber was called “negative”.

Positive: electron deficiency.

Negative: electron excess.

Coulomb (C)

Q = n · e

◦ Q of an electron: -1.6 · 10-19 C◦ Q of a proton: +1.6 · 10-19 C◦ Q of a neutron: 0

(+ or -) 1,6 * 10-19 * (6,02*10 23)=96320 C

the charge of one mole protons or electrons

In an isolated (closed) system:

◦ Charge is not created, only exchanged.

◦ Objects become charged because negative charge istransferred from one object to another.

The net charge of an isolated system remains constant.

!

!

Electrostatic Charging

Conductors: electrons have relatively high mobility.◦ Metals

◦ When a conductor is charged in a small region, the chargedistributes itself over the entire surface.

Insulators: electrons are more tightly bound to the atom.◦ Glass, rubber

◦ When insulators are charged by rubbing, only the rubbed area becomes charged.

There is no tendency for the charge to move to other regions of the material.

grounding

Electric Force and Electric Field

The magnitude of the force between q1 and q2 is described by Coulomb’s Law:

k= Coulomb constant (9,0 × 109 N∙m2 / C2)

F k q1q2

r2!

Two point charges of -1.0 µC and +2.0 µC are separated by a distance of 0.30 m. What is the electrostatic force on each particle?

An electric field exists in space around a charged object.◦ When another charged object enters this electric field, the

field exerts a force on the second charged object.

E: magnitude of the electric field

q0: positive test charge

k: Coulomb constant (9,0 × 109 N∙m2 / C2)

E F

q0 C

N

r 2E

kqUnit:

Electric fields are represented by electric field lines (imaginary).

direction?

touching?

Electric field vector represents the force directionof a small positive charge in the electric field.

+ -

The ‘density’ of field lines!

+ -

The ‘density’ of field lines determines the strength of the field.

Any excess charge on an isolated conductor residesentirely on the surface of the conductor

The electric field is zero everywhere inside acharged conductor

The electric field at the outer surface of a chargedconductor is perpendicular to the surface

Charge tends to accumulate at sharp points, orlocations of greatest curvature, on asymmetriccharged conductors (lightning rod!)

Lightning rod Faraday cage (cars, airplanes)

earth

Electrical Energy and Electric Potential

When 2 or more charges are brought closertogether or further apart, work is done, andenergy is expended or stored

Electrostatic potential energy:

Change in potential energy=Electricalpotential = Voltage

W: work done in bringing the test charge in from infinity

Unit: volt (J/C) V

V W

Q

V WAB

Q

Electronvolt

1 eV=1,602*10 -19 joule

Franck-Hertz-experiment

Cath.

An.

Photoelectric effect

Ekin = h f – W

h=6.63*10-34 m2kg/s

Capacitance and Dielectrics

Capacitors store electrical energy

Q: charge

V: voltage

C: capacitance(constant of proportionality)

unit: F (farad)

BatteryQ CV!

A: surface area

d: distance between plates

ε0 : permittivity of vacuum (8.85 × 10-12 C2/Nm2)

C 0 A

d!

What would be the area of the plates of a 1.0 F parallel-plate capacior with a plate separaion of 1.0 mm?

Closed electrical network (electrical network which has closed

loop giving a return path for the current).

Elements (devices) of the electrical circuit:

Source of the voltage (battery)

Transmission lines (wires)

Resistors

(Capacitors)

energy into Converts chemical electric energy.

Anode: positively chargedterminal of the battery.

charged Cathode: negativelyterminal of the battery.

Electromotive force voltage):

(electric electricpotential or

potential difference between theterminals of the battery.

Source of the voltage (electric potential) thatsupplies the electric energy throughconversation of other forms of energy.

Conductor which must possess mobilecharged particles e.g. ions, electrons.

Closed electrical circuit: gives a return pathfor the current.

Consider charges moving in a conductor – such as a wire. If an electric field is applied, there is a net flow of charges in the conductor.

Electric current (I): net charge flowing through the cross-sectional area (A)in time:

Unit of current: A (ampere)

The current flowing through a unit cross-sectional area is called Current Density:

Unit of current density:

I q

t

J I

A

C1A 1sec

m2

A

!

A current of 0.50 A flows in a circuit for 2.0 min. How much charge passes through a cross-sectional area of one of the connecting wires during this time?

Ohm’s Law and Resistance

Current is directly proportional to the voltage

The slope of the straight line gives the resistance (R) of the system

I ~ V

Resistance (R) is inverse proportional to the current

unit: Ohm (Ω)

I ~1

R

R V

I

Ohm’s law: shows the connection between current, voltage and resistance

UI R

U R I !(Ohmic conductor: obeys to Ohm’s Law)

UVR I

• Resistance comes from the collision of atoms and ions (that build up thematter) with the flowing electrons.

• It depends on:

- the kind of the matter– electrical resistivity (ρ)

- length of the conductor(l)

- the cross sectional area (A)

- temperature

• Electrical resistivity is temperature dependent (usually increases withincreasing temperature)

• Specific conductance (σ) is the inverse of electrical resistivity:

Origin of resistance

A

lR

1

Problem:If the specific conductance is 1000 1/(Ωm), the length of the conductor cable is 10 m,and it’s diameter is 1 cm, then how much is it’s resistance?

Electric Circuits

I. Kirchhoff's first law (current law), Kirchhoff's point rule, or Kirchhoff's

junction rule (or nodal rule).

The principle of conservation of electric charge implies that: At any node

(junction) in an electrical circuit, the sum of currents flowing into that

node is equal to the sum of currents flowing out of that node

II. This law is called Kirchhoff's (voltage law) second law, Kirchhoff's loop (or

mesh) rule, and Kirchhoff's second rule.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around

any closed network is zero

Kirchoff’s laws:*

*wikipedia

Series circuit◦ Resistors are connected end to

end.

◦ Theeach

current going through resistor is equal to the

current of the source.

◦ The voltage of the sourcedecreases at each resistor.

◦ The equivalent resistance (Rs) of the circuit (net resistance).

Rs R1 R2 R3

Parallel circuit◦ Resistors are connected with one end to another.

◦ The voltage drop on each resistor is equal to the voltage of the source.

◦ The current divides among the resistors proportionally.◦ The equivalent resistance (Rp) of the circuit (net

resistance).

1 11 1

R2 R3R p R1

Problem)Find the missing values of the table!

V0

R1 R2

R3

V0 (kV) 0.2

V1 (V) 90

I1 (A)

R1 (kΩ) 1

V2 (V)

I2 (A)

R2 (Ω)

V3 (V)

I3 (mA) 1000

R3 (Ω)

R net total

(Ω)

Thank you for the attention!