Pertemuan VPertemuan V

Dasar Teknik ElektroDasar Teknik Elektro

Resistor, Capasitor dan Resistor, Capasitor dan InduktorInduktor

ResistorsResistors Resistors can be either fixed Resistors can be either fixed

or variable in valueor variable in value Fixed resistorsFixed resistors come in a come in a

variety of different shapes, variety of different shapes, sizes and formssizes and forms

Axial lead resistors have the Axial lead resistors have the value of resistance printed on value of resistance printed on them or as a colour codethem or as a colour code

Surface mount resistors have Surface mount resistors have a numerical code indicating a a numerical code indicating a valuevalue

All resistors have a tolerance All resistors have a tolerance valuevalue

ResistorsResistors Variable resistorsVariable resistors

are called are called potentiometerspotentiometers

There is a fixed There is a fixed value of resistance value of resistance between two between two terminalsterminals

The moving part of The moving part of the potentiometer the potentiometer is called the wiperis called the wiper

ResistorsResistors Four band resistor Four band resistor

colour codecolour code 1st band provides the 1st band provides the

first digit of the codefirst digit of the code 2nd band provides the 2nd band provides the

second digit of the second digit of the codecode

3rd band is the 3rd band is the multipliermultiplier

4th band indicates the 4th band indicates the tolerance valuetolerance value

ResistorsResistorsResistor colour code calculationResistor colour code calculation

The first band red has a value The first band red has a value of 2of 2

The second band purple has a The second band purple has a value of 7value of 7

The third band has a The third band has a multiplier of x 10multiplier of x 10

The last band indicates a The last band indicates a tolerance value of tolerance value of +/-5%+/-5%

Resistance value is 270Ω +/-Resistance value is 270Ω +/-5%5%

2

7

x10

+/-5%

Resistors in Series Resistors in Series and Parallel Circuitsand Parallel Circuits

Resistors in circuitsResistors in circuits

To determine the current or To determine the current or voltage in a circuit that voltage in a circuit that contains multiple resistors, contains multiple resistors, the total resistance must first the total resistance must first be calculated.be calculated.

Resistors can be combined in Resistors can be combined in series or parallel.series or parallel.

Resistors in SeriesResistors in Series

When connected in series, the When connected in series, the total resistance (Rt) is equal to:total resistance (Rt) is equal to:

Rt = RRt = R11 + R + R22 + R + R3 3 +…+…

The total resistance is always The total resistance is always larger than any individual larger than any individual resistance.resistance.

Sample Sample ProblemProblem

10 V

15 Ω

10 Ω

6 ΩCalculate the Calculate the total current total current through the through the circuit.circuit.Rt = 15 Rt = 15 ΩΩ +10 +10 ΩΩ + + 6 6 ΩΩRt = 31 Rt = 31 ΩΩ

I = I = V/RV/Rtt

= 10 V/ 31 = 10 V/ 31 ΩΩ = =

0.32 0.32 AA

Since charge has only one path to Since charge has only one path to flow through, the current that passes flow through, the current that passes through each resistor is the same.through each resistor is the same.

The sum of all potential differences The sum of all potential differences equals the potential difference equals the potential difference across the battery. across the battery.

Resistors in SeriesResistors in Series

10 V

5 V

3 V

2 V

Resistors in ParallelResistors in Parallel

When connected in parallel, the When connected in parallel, the total resistance (Rt) is equal to:total resistance (Rt) is equal to:

1/Rt = 1/R1/Rt = 1/R11 + 1/R + 1/R22 + 1/R + 1/R33 +… +…

Due to this reciprocal Due to this reciprocal relationship, the total relationship, the total resistance is always smaller resistance is always smaller than any individual resistance.than any individual resistance.

Sample Sample ProblemProblem

12 Ω

4 Ω

6 Ω

Calculate the total Calculate the total resistance through resistance through this segment of a this segment of a circuit.circuit.1/Rt = 1/12 1/Rt = 1/12 ΩΩ +1/4 +1/4 ΩΩ + + 1/6 1/6 ΩΩ = 1/12 = 1/12 ΩΩ + 3/12 + 3/12 ΩΩ + +

2/12 2/12 ΩΩ1/R1/Rt t = 6/12 = 6/12 ΩΩ = = ½ ½ ΩΩ

Rt = 2 Rt = 2 ΩΩ

Since there is more than one Since there is more than one possible path, the current possible path, the current divides itself according to the divides itself according to the resistance of each path.resistance of each path.

smallest resistor = more current smallest resistor = more current

passespasses

largest resistor = least largest resistor = least current passescurrent passes

Resistors in ParallelResistors in Parallel

The voltage across each The voltage across each resistor in a parallel resistor in a parallel combination is the same. combination is the same.

Resistors in ParallelResistors in Parallel

10 V

10 V

10 V

10 V

Calculate the total Calculate the total resistance in the circuit resistance in the circuit

belowbelow

+ -

3 3 ΩΩ

2 2 ΩΩ

6 6 ΩΩ

4 4 ΩΩ

RRtottot = 3 = 3 ΩΩ + 2 + 2 ΩΩ = = 5 5 ΩΩ

RRtottot = 6 = 6 ΩΩ + 4 + 4 ΩΩ = = 10 10 ΩΩ

1/R1/Rtottot = 2/10 = 2/10 ΩΩ+ 1/10 + 1/10 ΩΩ = = 3/10 3/10 ΩΩ

RRtottot = 3 = 3 1/31/3ΩΩ

KAPASITOR KAPASITOR dan dan

DIELEKTRIKDIELEKTRIK

Contoh-contoh CapacitorContoh-contoh Capacitor

Contoh-contoh CapacitorContoh-contoh Capacitor

Pengertian KapasitorPengertian Kapasitor

Dua penghantar berdekatan yang dimaksudkan Dua penghantar berdekatan yang dimaksudkan untuk diberi muatan sama tetapi berlawanan untuk diberi muatan sama tetapi berlawanan jenis disebut jenis disebut kapasitorkapasitor..

Sifat menyimpan energi listrik / muatan listrik.Sifat menyimpan energi listrik / muatan listrik. KapasitasKapasitas suatu kapasitor ( suatu kapasitor (CC) adalah ) adalah

perbandingan antara besar muatan perbandingan antara besar muatan QQ dari salah dari salah satu penghantarnya dengan beda potensial satu penghantarnya dengan beda potensial VV antara kedua pengahntar itu.antara kedua pengahntar itu.

Kegunaan KapasitorKegunaan Kapasitor Untuk menghindari terjadinya loncatan listrik Untuk menghindari terjadinya loncatan listrik

pada rangkaian2 yang mengandung kumparan pada rangkaian2 yang mengandung kumparan bila tiba2 diputuskan arusnya.bila tiba2 diputuskan arusnya.

Rangkaian yang dipakai untuk menghidupkan Rangkaian yang dipakai untuk menghidupkan mesin mobilmesin mobil

Untuk memilih panjang gelombang yang Untuk memilih panjang gelombang yang ditangkap oleh pesawat penerima radio.ditangkap oleh pesawat penerima radio.

Bentuk kapasitorBentuk kapasitor Kapasitor bentuk keping sejajarKapasitor bentuk keping sejajar Kapasitor bentuk bola sepusatKapasitor bentuk bola sepusat Kapasitor bentuk silinderKapasitor bentuk silinder

DIELEKTRIKDIELEKTRIKDielektrik adalah suatu lempengan tipis yang diletakkan di antara kedua pelat kapasitor. Jika di antara keping + dan keping – diisi dengan bahan dielektrik (isolator), kuat medan listrik di antara keping akan menurun dan kapasitansi akan naik.

00 Cd

AC

Beberapa alasan penggunaan dielektrik adalah :

Memungkinkan untuk aplikasi tegangan yang lebih tinggi (sehingga lebih banyak muatan).

Memungkinkan untuk memasang pelat menjadi lebih dekat (membuat d lebih kecil).

Memperbesar nilai kapasitansi C karena K>1.

Dengan adanya suatu lembaran isolator (“dielectric”) yang ditempatkan di antara kedua pelat, kapasitansi akan meningkat dengan faktor K, yang bergantung pada material di dalam lembaran. K disebut sebagai konstanta dielektrik dari material.

dielectric

Karenanya C = K0A / d secara umum adalah benar karena K bernilai 1 untuk vakum, dan mendekati 1 untuk udara. Kita juga dapat mendefinisikan = K 0 dan menuliskan C = A / d. disebut sebagai permitivitas dari material

C = K0A / d

Kapasitas KapasitorKapasitas Kapasitor

Bila luas masing2 Bila luas masing2 keping keping AA, , maka :maka :

Tegangan antara kedua Tegangan antara kedua keping :keping :

Jadi kapasitas kapasitor untuk ruang hampa Jadi kapasitas kapasitor untuk ruang hampa adalah :adalah :

A

QE

00

A

dQdEV

0

..

d

A

V

QC 00

+

+

+

+

+q -q

A

d

E

-

-

-

-

Bila di dalamnya diisi bahan lain yang mempunyai Bila di dalamnya diisi bahan lain yang mempunyai konstanta dielektrik konstanta dielektrik KK, maka kapasitasnya menjadi, maka kapasitasnya menjadi

Hubungan antara Hubungan antara CC00 dan dan CC adalah : adalah :

Kapasitor akan berubah kapasitasnya bila :Kapasitor akan berubah kapasitasnya bila : KK , , A A dan dan d d diubahdiubah

Dalam hal ini Dalam hal ini CC tidak tergantung tidak tergantung QQ dan dan VV, hanya , hanya merupakan perbandingan2 yang tetap saja. merupakan perbandingan2 yang tetap saja. Artinya meskipun harga Artinya meskipun harga QQ diubah2, harga diubah2, harga CC tetap. tetap.

d

AKC 0

00 karena KKCC

Hubungan KapasitorHubungan Kapasitor

a.a. Hubungan SeriHubungan Seri

Kapasitor yang dihubungkan seri akan Kapasitor yang dihubungkan seri akan mempunyai muatan yang sama.mempunyai muatan yang sama.

321

1111

CCCCs

sadcdbcab C

QV

C

QV

C

QV

C

QV ; ; ;

321

321 QQQQ

b.b. Hubungan ParalelHubungan Paralel

Kapasitor yang dihubungkan paralel, tegangan Kapasitor yang dihubungkan paralel, tegangan antara ujung2 kapasitor adalah sama, antara ujung2 kapasitor adalah sama, sebesar sebesar VV..

321 CCCC p

; ; ; ; 332211 VCQVCQVCQVCQ p

Energi KapasitorEnergi Kapasitor

Sesuai dengan fungsinya, maka kapasitor yang Sesuai dengan fungsinya, maka kapasitor yang mempunyai kapasitas besar akan dapat mempunyai kapasitas besar akan dapat menyimpan energi yang lebih besar pula.menyimpan energi yang lebih besar pula.

Persamaannya :Persamaannya :

QVCVW 212

21

KAPASITORKAPASITORSecara umum Kapasitor terdiri atas dua keping konduktor yang saling sejajar dan terpisah oleh suatu bahan dielektrik ( dari bahan isolator) atau ruang hampa.

Secara umum Kapasitor terdiri atas dua keping konduktor yang saling sejajar dan terpisah oleh suatu bahan dielektrik ( dari bahan isolator) atau ruang hampa.

Bahan dielektrik

Antara dua keping dihubungkan dengan beda potensial V dan menimbulkan muatan listrik sama besar pada masing-masing keping tetapi berlawanan tanda.

Antara dua keping dihubungkan dengan beda potensial V dan menimbulkan muatan listrik sama besar pada masing-masing keping tetapi berlawanan tanda.

Sumber Gambar : Haliday-Resnick-Walker

Luas =A

KapasitorKapasitor Sifat KapasitorSifat Kapasitor

1. Dapat menyimpan energi 1. Dapat menyimpan energi listrik, tanpa disertai reaksi listrik, tanpa disertai reaksi kimiakimia

2. Tidak dapat dilalui arus 2. Tidak dapat dilalui arus listrik DC dan mudah listrik DC dan mudah dilalui arus bolak-balikdilalui arus bolak-balik

3. Bila kedua keping 3. Bila kedua keping dihubungkan dengan beda dihubungkan dengan beda potensial, masing-masing potensial, masing-masing bermuatan listrik sama bermuatan listrik sama besar tapi berlawanan besar tapi berlawanan tanda. tanda.

Hal.: 29Isi dengan Judul Halaman

Terkait

Simbol Kapasitor

+V

+Q -Q

KapasitorKapasitor Kapasitas kapasitor (C) Kapasitas kapasitor (C)

menunjukkan besar menunjukkan besar muatan listrik pada muatan listrik pada masing-masing keping bila masing-masing keping bila kedua keping mengalami kedua keping mengalami beda potensial 1 voltbeda potensial 1 volt

Hal.: 30Isi dengan Judul Halaman

Terkait

+V

+Q -Q

V

V

QC Q = nilai muatan listrik pada masing-

masing kepingV = beda potensial listrik antar keping ( volt)C = kapasitas kapasitor (Farad = F )

Kapasitas kapasitorKapasitas kapasitor

Hal.: 31

Ruang hampa atau udara

Luas =A

V

QC

d

xAεC o

C = kapasitas kapasitor (Farad= F)

d = Jarak antar keping (meter)

A = luas salah satu permukaan yang saling berhadapan (meter 2 )

o = permitivitas udara atau ruang hampa

( 8.854 187 82 · 10-12 C/vm )

dAεQ

Q

Exd

QC

o

x

Kapasitas kapasitorKapasitas kapasitor

Hal.: 32

Bahan dielektrik

Luas =A

d

εxAC

= permitivitas bahan dielektrik ( C/vm )

K.εε o

Kapasitas kapasitor yang terdiri atas bahan dielektrik

K = tetapan dielektrik (untuk udara atau ruang hampa K = 1 )

Rangkaian KapasitorRangkaian Kapasitor Rangkaian seri Rangkaian seri

Hal.: 33

+V

+Q1 -Q1 +Q2 -Q2

1. Kapasitas gabungan kapasitor (Cg ), kapasitas kapasitor pertama (C1), kapasitor kedua (C2) memenuhi :

2. Muatan listrik yang tersimpan pada rangkaian = muatan listrik pada masing-masing kapasitor. Q = Q1 + Q2 dan Q1 = Q2

3. Tegangan listrik antar ujung rangkaian(V), tegangan pada kapasitor pertama(V1 ) dan kapasitor kedua(V2 ) memenuhi:V = V1 + V2

1. Kapasitas gabungan kapasitor (Cg ), kapasitas kapasitor pertama (C1), kapasitor kedua (C2) memenuhi :

2. Muatan listrik yang tersimpan pada rangkaian = muatan listrik pada masing-masing kapasitor. Q = Q1 + Q2 dan Q1 = Q2

3. Tegangan listrik antar ujung rangkaian(V), tegangan pada kapasitor pertama(V1 ) dan kapasitor kedua(V2 ) memenuhi:V = V1 + V2

21g C

1

C

1

C

1

Rangkaian KapasitorRangkaian Kapasitor Rangkaian seri Rangkaian seri

Hal.: 34

+V = 6 volt

+Q -Q +Q -Q

C1 = 2 F C2 = 3 F

ContohContoh1. Kapasitas gabungan kapasitor :

Cg = 6/5 = 1,2 F2. Muatan listrik pada rangkaian = 1,2 F x 6V = 7,2 C Pada kapasitor satu = 7,2 C Pada kasitor kedua = 7,2 C3. Tegangan liatrik pada kapasitor satu = 3,6 V Pada kapasitor dua = 2,4 V

1. Kapasitas gabungan kapasitor :

Cg = 6/5 = 1,2 F2. Muatan listrik pada rangkaian = 1,2 F x 6V = 7,2 C Pada kapasitor satu = 7,2 C Pada kasitor kedua = 7,2 C3. Tegangan liatrik pada kapasitor satu = 3,6 V Pada kapasitor dua = 2,4 V

6

23

3

1

2

1

C

1

g

Rangkaian KapasitorRangkaian Kapasitor Rangkaian paralel Rangkaian paralel

Hal.: 35

+V

+Q1 -Q1

+Q2 -Q2

1. Tegangan pada kapasitor pertama (V1), kapasitor kedua (V2) dan tegangan sumber (V) masing-masing sama besar. V1 = V2 = V

2. Muatan listrik yang tersimpan pada rangkaian memenuhi Q = Q1 + Q2

3. Kapasitas gabungan kapasitor mmenuhi : Cg = C1 + C2

Rangkaian KapasitorRangkaian Kapasitor Rangkaian paralel Rangkaian paralel

Hal.: 36Isi dengan Judul Halaman

Terkait

+

+Q1 -Q1

+Q2 -Q2

1. Tegangan pada kapasitor pertama (V1) dan kapasitor kedua (V2) adalah V1 = V2 = 6 volt

2. Kapasitas gabungan kapasitor adalah Cg = C1 + C2 = 2F + 3F = 5F

3. Muatan listrik yang tersimpan pada rangkaian memenuhi Q = Cg xV = 5F x 6V = 30CQ1 = C1 x V = 2Fx6V = 12C

Q2 = C2 x V = 3Fx6V = 18C

Contoh Contoh

C1 = 2 F

C2 = 3 F

V = 6 volt

Energi Listrik yang Tersimpan Energi Listrik yang Tersimpan pada Kapasitorpada Kapasitor

Grafik hubungan tegangan (V) dengan muatan listrik yang Grafik hubungan tegangan (V) dengan muatan listrik yang tersimpan pada kapasitor (Q) tersimpan pada kapasitor (Q)

Hal.: 37Isi dengan Judul Halaman

Terkait

V(volt)

Q(Coulomb)

Q

V

Nilai energi listrik yang tersimpan pada kapasitor yang bermuatan listrik Q = luas daerah Dibawah garis grafik Q-V (yang diarsir ).

QV2

1W

Energi Listrik yang Tersimpan Energi Listrik yang Tersimpan pada Kapasitorpada Kapasitor

Hal.: 38Isi dengan Judul Halaman

Terkait

(CV)V2

1W

+V

Sebuah kapasitor yang memiliki kapasitas C dihubungkan dengan tegangan V.

CKarena Q = C.V, maka

2CV2

1W

W = Energi listrik yang tersimpan pada kapasitor ( Joule )

Keterangan : Q = muatan listrik kapasitor ( Coulomb)

C = Kapasitas kapasitor ( farad)

V = tegangan listrik antar keping kapasitor ( Volt)

InductorsInductorsEnergy Storage DevicesEnergy Storage Devices

Objective of LectureObjective of Lecture

DescribeDescribe The construction of an inductorThe construction of an inductor How energy is stored in an inductorHow energy is stored in an inductor The electrical properties of an inductorThe electrical properties of an inductor

Relationship between voltage, current, and Relationship between voltage, current, and inductance; power; and energyinductance; power; and energy

Equivalent inductance when a set of Equivalent inductance when a set of inductors are in series and in parallelinductors are in series and in parallel

InductorsInductors

Generally - coil of conducting wireGenerally - coil of conducting wire Usually wrapped around a solid core. If Usually wrapped around a solid core. If

no core is used, then the inductor is no core is used, then the inductor is said to have an ‘air core’.said to have an ‘air core’.

http://bzupages.com/f231/energy-stored-inductor-uzma-noreen-group6-part2-1464/

SymbolsSymbols

http://www.allaboutcircuits.com/vol_1/chpt_15/1.html

Alternative Names for Alternative Names for Inductors Inductors

Reactor- inductor in a power gridReactor- inductor in a power grid Choke - designed to block a particular Choke - designed to block a particular

frequency while allowing currents at lower frequency while allowing currents at lower frequencies or d.c. currents throughfrequencies or d.c. currents through Commonly used in RF (radio frequency) circuitryCommonly used in RF (radio frequency) circuitry

Coil - often coated with varnish and/or wrapped Coil - often coated with varnish and/or wrapped with insulating tape to provide additional with insulating tape to provide additional insulation and secure them in placeinsulation and secure them in place A winding is a coil with taps (terminals).A winding is a coil with taps (terminals).

Solenoid – a three dimensional coil. Solenoid – a three dimensional coil. Also used to denote an electromagnet where the Also used to denote an electromagnet where the

magnetic field is generated by current flowing magnetic field is generated by current flowing through a toroidal inductor.through a toroidal inductor.

Energy StorageEnergy StorageThe flow of current through an inductor The flow of current through an inductor

creates a magnetic field (right hand rule).creates a magnetic field (right hand rule).

If the current flowing through the If the current flowing through the inductor drops, the magnetic field will inductor drops, the magnetic field will also decrease and energy is released also decrease and energy is released through the generation of a current.through the generation of a current.

http://en.wikibooks.org/wiki/Circuit_Theory/Mutual_Inductance

B field

Sign ConventionSign Convention• The sign convention used with The sign convention used with

an inductor is the same as for a an inductor is the same as for a power dissipating device.power dissipating device.

• When current flows into the positive When current flows into the positive side of the voltage across the side of the voltage across the inductor, it is positive and the inductor, it is positive and the inductor is dissipating power. inductor is dissipating power.

• When the inductor releases energy When the inductor releases energy back into the circuit, the sign of the back into the circuit, the sign of the current will be negative.current will be negative.

Current and Voltage Current and Voltage RelationshipsRelationships

11t

t

LL

L

o

dtvL

i

dt

diLv

L , inductance, has the units of Henries (H)L , inductance, has the units of Henries (H)

1 H = 1 V-s/A1 H = 1 V-s/A

Power and EnergyPower and Energy

11

1

t

t

LL

t

t

LL

t

t

LLLLL

oo

o

diiLdtidt

diLw

dtiLiivp

InductorsInductors

Stores energy in an magnetic field Stores energy in an magnetic field created by the electric current created by the electric current flowing through it.flowing through it. Inductor opposes change in current Inductor opposes change in current

flowing through it.flowing through it. Current through an inductor is continuous; Current through an inductor is continuous;

voltage can be discontinuous.voltage can be discontinuous.

http://www.rfcafe.com/references/electrical/Electricity%20-%20Basic%20Navy%20Training%20Courses/electricity%20-%20basic%20navy%20training%20courses%20-%20chapter%2012.htm

Calculations of LCalculations of L

For a solenoid (toroidal inductor)For a solenoid (toroidal inductor)

N is the number of turns of wireN is the number of turns of wireA is the cross-sectional area of the toroid in mA is the cross-sectional area of the toroid in m22..r r is the relative permeability of the core materialis the relative permeability of the core materialoo is the vacuum permeability ( is the vacuum permeability (44ππ × 10 × 10-7-7 H/m)H/m)ll is the length of the wire used to wrap the toroid is the length of the wire used to wrap the toroid

in metersin meters

ANAN

L or 22

WireWire

Unfortunately, even bare wire has inductance.

d is the diameter of the wire in meters.

Hxd

L 710214ln

Properties of an InductorProperties of an Inductor

Acts like an short circuit at steady state Acts like an short circuit at steady state when connected to a d.c. voltage or when connected to a d.c. voltage or current source.current source.

Current through an inductor must be Current through an inductor must be continuouscontinuous There are no abrupt changes to the current, but there can There are no abrupt changes to the current, but there can

be abrupt changes in the voltage across an inductor.be abrupt changes in the voltage across an inductor.

An ideal inductor does not dissipate An ideal inductor does not dissipate energy, it takes power from the circuit energy, it takes power from the circuit when storing energy and returns it when when storing energy and returns it when discharging.discharging.

Properties of a Real Properties of a Real InductorInductor

Real inductors do dissipate energy Real inductors do dissipate energy due resistive losses in the length of due resistive losses in the length of wire and capacitive coupling wire and capacitive coupling between turns of the wire.between turns of the wire.

Inductors in SeriesInductors in Series

LLeqeq for Inductors in for Inductors in SeriesSeries

i

4321eq

4321

4433

2211

4321

Ldt

didt

di

dt

di

dt

di

dt

di

dt

di

dt

di

dt

di

dt

di

LLLL

Lv

LLLLv

LvLv

LvLv

vvvvv

eqin

in

in

Inductors in ParallelInductors in Parallel

LLeqeq for Inductors in for Inductors in ParallelParallel

i

14321eq

t

t

t

t4

t

t3

t

t2

t

t1

t

t44

t

t33

t

t22

t

t11

4321

1111L

vdt1

vdt1

vdt1

vdt1

vdt1

vdt1

vdt1

vdt1

vdt1

1

o

1

o

1

o

1

o

1

o

1

o

1

o

1

o

1

o

LLLL

Li

LLLLi

Li

Li

Li

Li

iiiii

eqin

in

in

General Equations for LGeneral Equations for Leqeq

Series CombinationSeries Combination Parallel CombinationParallel Combination If S inductors are in If S inductors are in

series, thenseries, then If P inductors are in If P inductors are in

parallel, then:parallel, then:

1

1

1

P

p peq LL

S

sseq LL

1

SummarySummary Inductors are energy storage devices.Inductors are energy storage devices. An ideal inductor act like a short circuit at An ideal inductor act like a short circuit at

steady state when a DC voltage or current steady state when a DC voltage or current has been applied.has been applied.

The current through an inductor must be a The current through an inductor must be a continuous function; the voltage across an continuous function; the voltage across an inductor can be discontinuous.inductor can be discontinuous.

The equation for equivalent inductance forThe equation for equivalent inductance for

inductors in seriesinductors in series inductors in parallelinductors in parallel

1

1

1

P

p peq LL

S

sseq LL

1