1

Chapter 2Fundamentals of electric circuits

Jaesung Jang

Electricity and CurrentKCL and KVL

Resistance and Ohm’s lawVoltage and Current Dividers

Practical Voltage and Current Sources

2

Electrons and Protons in the Atom• Example: A hydrogen atom contains one proton (양성자) in its nucleus. This is

balanced by one orbiting electron (전자). A hydrogen atom contains no neutrons in its nucleus.

• Electrons are distributed in orbital rings around the nucleus.

• Charge of an electron and proton– The charge of a single electron, or qe, is 0.16 × 10−18 C (coulomb) -> qe = - 0.16 × 10−18 C

where “-” indicates the charge is negative.– The charge of a single proton, qP, = + 0.16 × 10−18 C (->positive charge). – 1 coulomb (C) is equal to the charge quantity (전하량) (Q) of 6.25 × 1018 electrons or

protons.

3

Structure of the Atom• Atomic Number

– The atomic number (원자번호) of an element is the number of protonsin the nucleus of the atom balanced by an equal number of orbiting electrons.

– The number of electrons in orbit around the nucleus of a neutral atom is equal to the number of protons in the nucleus. (-> electrically neutral)

• Orbital Rings– Electrons are contained in successive rings beyond the nucleus. The

rings are called K, L, M, N, O, P, and Q, respectively.– Each ring has a maximum number of electrons for stability. They are:

�K ring = 2 electrons.�L ring = 8 electrons.�M ring = 8 or 18 electrons.�N ring = 8,18, or 32 electrons.

�O ring = 8 or 18 electrons�P ring = 8 or 18 electrons�Q ring = 8 electrons

4

Structure of the Atom (Cont.)• The electron valence of an atom is the number of electrons in the

incomplete outermost shell. The valence indicates how easily the atom can gain or lose electrons to make a complete (stable) outermost ring.

• The valence electrons below are weakly bound to the nucleus (unstable). The electrons in the outermost ring can escape freely from the atom due to a certain force (e.g. electric fields). That is, they become free electrons(자유전자).

• Free electrons can move from one atom to the next and are the basis of electric current.

29 protonsatomic number = 29

29 electrons(net charge = 0)

1 valence electron

29 protonsatomic number = 29

29 electrons(net charge = 0)

1 valence electron

free electrons

positive charge

+-electric fields

5

Current• The charge in motion due to

electric fields is an electric current.

• Current is defined as the time rate of change of electric charges (here positive charge is considered.)

• The current is I = dq/dt.– The unit of electric current is the

ampere (A).– 1 A = 6.25 × 1018 electrons

(1C)/sec.

6

Conductor, Insulator, & Semiconductor• Conductor (도체) has a great number of free electrons• Examples of conductors include:

– Silver, copper, aluminum

• Insulator (Dielectric) (부도체) only a few free electrons (자유전자가거의없다)• 정전기 (Static electricity)• Examples of insulators include:

– Glass, plastic, rubber.

• Semiconductors (반도체) are materials that are neither good conductors nor good insulators. (도체와부도체의중간 -> 반도체)

• Examples of semiconductors include:– Carbon, silicon, germanium

7

Mechanical & Electrical Analogy

Gravitational field g

Stone

Ground

Electric fieldE

Positive charge

Electric ground

Distance

Gravitational field Move the stone

F/a = m

Electric field Move the electron

V/i = R

PotentialDifference(volt)

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Potential difference

• Two unlike charges generate the electric field where potential difference is a measure of strength of the electric field. (Imagine a battery!)

– The volt is the unit of potential difference.

• The potential difference (or voltage) between two points equals 1 volt when 1 J of energy is expended in moving 1 C of charge between those two points.

– 1 V = 1 J / 1 C

• Analogy: A 1 kg stone falling from 10 m height is faster at the ground than from 1 m height (중력[위치에너지] 에의한물체의떨어짐). Height ~ Voltage.

+

-

EBattery+

-

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The Closed Circuit• A circuit can be defined as a path

for current flow. Any circuit has three key elements:1. There must be a source of

potential difference. Without the applied voltage, current cannot flow.

2. There must be a complete pathfor current flow.

3. The current path normally has resistance, either to generate heat or limit the amount of current.

A closed circuit(current is flowing)

Circuit diagram

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An open circuit(no current is flowing)

The Open and Short Circuit

• Open and Short Circuits– When a current path is broken

(incomplete) the circuit is said to be open. The resistance of an open circuit is infinitely high. There is no current in an open circuit.

– When the current path is closed but has no resistance, the result is a short circuit. Short circuits can result in too much current due to no resistance.

11

Ideal Voltage Source• Ideal voltage source: it provides a

prescribed voltage (fixed) across its terminals irrespective of the currentflowing through it.

• Note that by convention, current is considered as the motion of positive charges. (load ~ resistance)

Current

Voltage

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Ideal Current Source

• Ideal current source: it provides a prescribed current to any circuit connected to it irrespective of the voltage flowing through it.

Voltage

Current

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Dependent (Controlled) Source

• Dependent (controlled sources): Current or voltage output is a function of some other voltage or current in a circuit

Current or voltage source

14

Branch and Node

• Branch is any portion of a circuit with two terminals connected to it.• Node is the junction of two or more branches. (two branches -> trivial node)

15

Loop and Mesh

• Loop is any closed connection of branches.• Mesh is a loop that does not contain other loops.

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Kirchhoff’s Current Law (KCL)• Charge cannot be created but must be

conserved. -> For any nodes of an electric circuit, the (algebraic) sum of all branch currents leaving the nodes is zero at any time.

• Plus sign: current direction points away from a node.

• Kirchhoff’s Current Law (KCL) on a node may also be stated as

∑ IP = 0

+

+_

For node P, IA+IB-IC=0

IA

P

IB

IC

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Kirchhoff’s Voltage Law (KVL)• A loop is any closed path in a circuit.

• KVL: For any loops of an electric circuit, the algebraic sum of the branch voltages around the loop is zero at any time. -> ΣV = 0 on a loop.

• Plus sign: voltage directions (Not the current direction) agree with “loop direction”.

Generalized representation of circuit elements

Loop direction

Loop = VoltageVoltage sign:

positive +

Loop direction

Loop ≠ Voltage Voltage sign:

negative -

Resistors, Inductors, Capacitors, or Transformers

What about voltage source?

i

V

+

_

a

b

V=Vab

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Example

0

0

0

543

422

3211

=++−=−+−

=+++−

VVV

VVV

VVVV

S

S

For clockwise loops

Loop A

Loop B

Loop C

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Resistance and Ohm’s Law• Resistance is the opposition to the

flow of current. For example, atoms can obstruct the path of electrons.

• Voltage and current have a certain relationship (i-v characteristic) because of resistance.

• Nonlinear resistance: i=f(v) v• Linear resistance: i=kv, where k is a

constant – Ohm’s law -> v=i R or i=G v – R (unit: Ohm) and G (unit:

Siemens) are constants.

A

lR ρ=

tyconductivi :

yresistivit :

σρ

econductanc :

resistance :

G

R

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Resistor• A component manufactured to have a specific value of resistance is called a resistor.• The two main considerations when buying a resistor are its resistance, R, in ohms

(with tolerance) and its power rating, P, in Watts. – The resistance, R, provides the required reduction in current or the desired drop in voltage.– The power rating indicates the amount of maximum power the resistor can safely work. (Ex.

½ power, ¼ power, 1 power)

– Exceeding the power rating leads to overheating and burning.

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Resistor Color Coding

x10color value

0 Black1 Brown2 Red3 Orange4 Yellow5 Green6 Blue7 Violet8 Gray9 White

Color Code Gold: -1 Silver: -2

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Electric Power

• Battery generates electric power (=work or energy per unit time).

• Resistor dissipates electric power as a form of heat due to collision of electrons and atoms.

• Power “dissipated”= voltage x current -> positive values for power consumption elements (e.g. resistor, inductor, conductor, etc.)

• P=Vi = i2R = v2/R

• The generated power is equal to the sum of the power dissipated by each resistance.

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Series Circuit and Voltage Dividers

Series circuit

V1

I1

R1

R2

I2

V2

V1: V2 :V3 = R1: R2: R3

I1= I2 = I3

V1=R1

V2=R2

VT

RT = R1+ R2 + R3

VT = V1+ V2 +V3

VT

VT

R3

I3

V3

R1+ R2 + R3

R1+ R2 + R3

V3=R3 VTR1+ R2 + R3

• Characteristics of a Series Circuit

– The current is the same everywhere in a series circuit.

– The total (equivalent) resistance is equal to the sum of the individual resistance values.

– The total voltage is equal to the sum of the IR voltage drops across the individual resistances.

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Parallel circuit

I1:I2:I3 = 1/R1: 1/R2 :1/R3

V1

I1

R1 R3

I3

V3

I1=1/R1

I2=1/R2

V1= V2 = V3IT

IT = I1+ I2 + I3

1/RT = 1/R1+ 1/R2 +1/R3

IT`

ITV2

I2

R2

I2=1/R3 IT

1/R1+ 1/R2 +1/R3

1/R1+ 1/R2 +1/R3

1/R1+ 1/R2 +1/R3

Parallel Circuit and Current Dividers • Characteristics of a Parallel

Circuit– Voltage is the same across each

branch.– The total current is equal to the

sum of the individual branch currents.

– The reciprocal of total (equivalent) resistance is equal to the sum of the reciprocal of individual resistance values.

– The equivalent resistance (total resistance) (REQ=RT) is less than the smallest branch resistance. The term equivalent resistance refers to a single resistance that would draw the same amount of current as all of the parallel connected branches.

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Series circuit

V1

I1

R1

R2

I2

V2

V1: V2 :V3 = R1: R2: R3

Parallel circuit

I1:I2:I3 = 1/R1: 1/R2 :1/R3

V1

I1

R1 R3

I3

V3

I1= I2 = I3

V1=R1

V2=R2

I1=1/R1

I2=1/R2

V1= V2 = V3

VT

IT

RT = R1+ R2 + R3

VT = V1+ V2 +V3

IT = I1+ I2 + I3

1/RT = 1/R1+ 1/R2 +1/R3

Voltage Dividers & Current Dividers

VT

VT

IT`

IT

R3

I3

V3

R1+ R2 + R3

R1+ R2 + R3

V3=R3 VTR1+ R2 + R3

V2

I2

R2

I2=1/R3 IT

1/R1+ 1/R2 +1/R3

1/R1+ 1/R2 +1/R3

1/R1+ 1/R2 +1/R3

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Practical Voltage & Current Source

• Real voltage source has the internal resistance inside.

• The internal resistance poses a limit to the maximum current in a practical voltage source and maximum voltage in a practical current source.

SSSL

LLS

SL

SLLS

SSL

SL

rirR

RRi

rR

rRi

irR

ri

+=

+==→

+=

υ

In the practical current source

27

Ohmmeter & Ammeter• Ohmmeter:

– The resistance of an element can be measured only when the element is disconnected from any other circuit.

• Ammeter– The ammeter must be placed in

series with the element to be measured.

– The ammeter should not restrict the flow of current (induce another voltage drops) or else it will not be measuring the true current flowing in the circuit. An ideal ammeter has zero internal resistance.

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Voltmeter

• Voltmeter– The voltmeter must be

placed in parallel with the element to be measured.

– The voltmeter should not draw any current or else it will not be measuring the true current flowing in the circuit. An ideal voltmeter has infiniteinternal resistance.

• Wattmeter– Combination of

voltmeter and ammeter.

Read conclusion at pp. 48!!!!