Chapter 1. Fundamental Electrical Concepts

Chapter 1

Fundamental Electrical Concepts

Charge, current, voltage, power circuits, nodes, branches

Branch and node voltages, Kirchhoff Laws

Electrical Charge

Relates to electrical forces between particles Bipolar: positive or negative charge

Electrical effects due to movement and

separation of charge

Is measured in coulomb [C]

Symbol Q (static) or q (time varying)

Discrete: electron has charge e = -1.602 x 10-19 _C

Coulomb’s law: Q_{1 Q} 2 1

r

_r

Electrical Current

Moving electrical charge

Controlled movement and separation of charges determines function of circuit or system

Current can be:

Function of time: alternating current (ac) Constant: direct current (dc)

Symbol I (dc) or i (ac) Unit: ampere (A)

+ ₊ + + + + + + + + – – – – – – – – – – Migration of electrons

Conducting source with Conducting target wire

(current = stroom)

ampere =

Electrical Current

Conducting source with excess electrons Conducting target depleted of electrons wire + ₊ + + + + + + + + – – – – – – – – – – + ₊ + + + + + + + + + ₊ + + + + + + + + – – – – – – – – – – – – – – – – – – – – Migration of electrons

Conducting source with excess electrons Conducting target depleted of electrons wire + ₊ + + + + + + + + – – – – – – – – – – excess electrons shortage of electrons + pole - pole Positive current Electron flow battery

Electrical Current

Current: amount of charge being transferred per unit time: ampere = coulomb/second.

q q q q A q ∆t ∆q q t q I ∆ ∆ = dt dq i = (stroomsterkte)

Electrical Current

Current follows a path

has a direction: arrow and sign

and magnitude

-2 mA

-2 mA 2 mA 2 mA

Voltage or Potential Difference

Relates to the energy associated with charge transfer (current) unit: volt [V] symbol: V (dc) or v (ac) q w v_ab = ab + – v_ab a b

One volt is the amount of work (energy) it costs to transfer one coulomb of charge

Hydraulic Analogy

Voltage is an across-quantity Current is a through-quantity

Voltage across terminals a and b Current through a wire

Voltage and Current

+ – v_ab a b i

current voltage

Power

unit watt [W] = joule/second [J/s] symbols: P, p §1.4 second work = p

Power = Rate of Work

= amount of work divided by time it takes

i x v p = voltage x current = second charge x charge work =

Unassociated

Associated: into plus terminal, leaving minus terminal

+ – v i

Reference Directions

☺

Power Direction

Lamp power: ? >0 ⇒ absorbing

<0 ⇒ releasing

Note: total power = 0!

I₁ V = (-0.02)(3) = -0.06 I V = (0.02)(3) = 0.06

Circuit Diagram

Bierthermometer

All different schematics but identical circuits

Circuit Diagram

Only gives connectivity

Form or shape is not important

32

Node

Elements are connected together

Connections are called nodes (knooppunten)

Nodes are drawn as line segments in circuit diagram

Connected line segments form a node

One node connects two or more elements

Node has unique potential (Circuit behavior follows from

potential (voltage) difference between nodes!)

Circuit Diagram

dot jump _gap cross

shift √ x x x 2 3 3 3 dot jump gap cross connection # nodes not prefered

Node Names

Nodes often have a unique

identifier or name or number or label or ...

a c d b e1 e2 e3 e4 e5 AMP INPUT OUTPUT COMMON 1 2 3 Idem elements Other annotations: Whatever is useful

Element values and type numbers, voltage, current, power, noise and any other relevant signal property, etc.

Path and Branch

Path (pad): trace of adjoining two-terminal elements

Branch (tak): a path that connects two nodes (and no more)

What are some branches? a - e1 - b What are some paths?

a - e1 - b - e2 - c a - e3 - d - e4 - b a c d b e1 e2 e3 e4 e5

Branch Voltages and Currents

Voltage across a branch (voltage is across-quantity)

Current through a branch (current is through-quantity)

a c d b e + + -V_ab V_e §1.6

Can use two node names or element name to specify a branch and branch voltage

Node Voltages

Do they exist?

same branch voltages imply same behavior

NO

Only potential differences are important Voltage = potential difference

Node voltage can not be defined unambiguously

10V 15V 30V _20V 110V 115V 130V 120V _-5V 0V 15V _5V

V_x ≡ V_x-reference

Node Voltages

Do they exist?

YES

Only when one arbitrary but specific node is chosen as reference node with a potential of 0V

Identical branch voltages Identical currents

Identical behavior

reference node = ground node = common node symbols: a c d b + -V_c 0V

Reference Node is Arbitrary

5V

2V

+3V

May choose one arbitrary

node as reference (0V)

One choice may be much more convenient for

calculation than other -a b c + 2V + 3V -d a b c V_c ? V_b ? d a b c V_b ? V_d ?

Loops

Loop (lus): closed path, begin node same as end node

How many loops?

a b d a b c d b c b a d c a c d b e §1.6

Voltage Drops

Voltage drop (spanningsval): difference in potential between two nodes along a path

!

Voltage Drops

Voltage drop (spanningsval): difference in potential between two nodes along a path

Take care of positive and negative sign reference

a b c d + V1 - + V2 - - V3 + V_ab = V_ac = V_ad = V_a – V_b = V₁ V_a – V_c = (V_a – V_b) + (V_b – V_c) = V₁ + V₂ V_a – V_d = (V_a – V_b) + (V_b – V_c) + (V_c – V_d) = V₁ + V₂ – V₃ voltage drop node potential

Kirchhoff’s Voltage Law (Spanningswet)

KVL: The algebraic sum of the

branch voltage drops around any loop (= closed path) is zero

v_c v_b v_a v₁ v₂ v₄ v₃ v_d + + + + -- - KVL: v4 – v5 – v2 = 0 v₄ – v₅ – v₂ = (v_b – v_d) – (v_c – v_d) – (v_b – v_c) = v_b – v_b – v_d + v_d – v_c + v_c = 0 v₅ + –

☺

Kirchhoff’s Current Law (Stroomwet)

KCL: The sum of the currents entering a node is equal to the sum of the currents leaving the node

5µA

2µA

3µA

Analogy:

Flow of water in pipes Cars at highway

Circuit Elements

Transistors, switches, resistors, capacitors and many more

At least two terminals

Constitutive Relation

(Constitutieve Relatie)

Terminal is connection point

Current can flow into or out of terminal (and element)

Potential difference can exist between terminals:

branch voltage

Relation between branch voltage and terminal current defines function of element

v = f(i), i = f--1_{(v) +}

– v

i

Note: functions of more than 1 variable in case of multi-terminal elements

Voltage v is defined

Current may have any value Idealized component

In practice, voltage will to some extend depend on current (and temperature, age, ...)

Voltage Source (Spanningsbron)

+ -v + -v ISO Symbol

Current Source (Stroombron)

Linear resistance: voltage proportional to current

Ohm’s Law (wet van Ohm)

v = i · R

R is resistance, unit: Ω (Ohm) = V/A

Resistance (Resistantie)

Resistance: The property of materials to impede the flow of electric charge

R

ISO symbol

i R

Resistor (Weerstand)

An actual circuit element having resistance as it’s main characteristic

Resistance means merely the electrical model of an ideal resistor

In practice, v = i R is only approximately or accurately valid in limited range of operating conditions (i.e. voltage, current, frequency, temperature)

Resistivity (Resistiviteit)

Resistance depends on

Material shape

of element

Consider rectangular resistive wire

Resistance R proportional to

– l length of resistor

– 1/A_R inverse of cross-sectional area

– ρ specific resistivity of material

A_R=hxw h i l w l R =

ρ

Current through Resistance

Resistors in Series (serieschakeling)

∑

equal to the sum of individual resistances

V kΩ mA v=iR TIP! equivalent R_eq = 3kΩ

Resistors in Series: Example

+ -V=6V 1kΩ I 2kΩ + -v₁ + -v₂ v = i R_eq (Ohms Law) 6V = I x 3k

Ω

Ω

See §1.2 for units and prefixes

V

Ω A

01 fundamental 14 TUE/EE 5CC00 netwerk analyse 04/05 - © NvdM

Bierthermometer LM3914N

Example

(Voltage Divider)

Example (Voltage Divider)

R

R

V

I

+

=

Note (KCL): all current flows from source through R₁ and R₂, no current flows into output terminals (it can’t go anywhere there)

V R R R IR V_out 2 1 2 2 = ₊ =

You will need this for first

programming assignment of the course “computation”

Potentiometers

Potentiometer = adjustable voltage divider

R (1−α)R

Potentiometers

Potentiometer

Typical audio amplifier:

1. Pre-amplifier 2. adjustable level reduction 3. power amplifier 1. 2. 3. R V + - Vout +

-Compute V_out as a function of α. Does V_out depend on R? (0 ≤ α ≤ 1 function of knob angle)

Summary

Charge, current, voltage Power

Circuits, Nodes, Branches, Loops Branch vs Node Voltages

KVL and KCL

Ideal Voltage and Current Sources

Resistance: Ohms Law, series connection Voltage division

Next: capacitor, inductor, combining ckt elements …