alternating current r-l-c series circuits

8/2/2019 Alternating Current R-l-c Series Circuits

1/56

3/20/12 AVADHUTA TRIVEDI

- PRESENTED BY

JAY B.THAKAR

M.TECH (POWER SYSTEM)

11

ALTERNATING CURRENT

CIRCUITS


2/56


OUTLINES

ResistorInductor

R L series circuit

CapacitorR C series circuit

R L C series circuit

Impedance

Phasor diagram

22


3/56

Click to edit Master subtitle style


WHAT ISRESISTOR?????

33


4/56


RESISTOR

A resistor is a two-terminalelectronic component

which implements electrical resistance as a circuit

element.

When a voltage V is applied across the terminals of a

resistor, a current I will flow through the resistor in

direct proportion to that voltage.

The reciprocal of the constant of proportionality isknown as the resistance R, since, with a given voltage

V, a larger value of R further "resists" the flow of

current.

Resistors can be either fixed or variable in value.44
http://en.wikipedia.org/wiki/Terminal_(electronics)http://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Direct_proportionhttp://en.wikipedia.org/wiki/Resistancehttp://en.wikipedia.org/wiki/Resistancehttp://en.wikipedia.org/wiki/Direct_proportionhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Terminal_(electronics)


5/56


(CONTD.)

Fixed resistors come in a variety of different shapes,

sizes and forms.

Resistors can be either fixed or variable in value

Fixed resistors come in a variety of different shapes,

sizes and forms

Axial lead resistors have the value of resistance printed

on them or as a colour code

Surface mount resistors have a numerical code indicatinga value

All resistors have a tolerance value.

Ohms Law for a resistor, R, in an AC circuit 55


6/56


TYPES OF RESISTORS

66


7/56


RESISTOR

77


8/56


THE VALUE OF

RESISTORS???The values of the resistor are calculated from the

colour of the bands. The values of the colours are

shown in Table on next slide

88

Four band resistor colour code

1st band provides the first digitof the code2nd band provides the second digitof the code

3rd band is themultiplier

4th band indicates the


9/56


99


10/56


CIRCUIT

Consider a circuitconsisting of an ACsource and a resistor

The graph shows the

current through and thevoltage across theresistor

The current and the

voltage reach theirmaximum values at thesame time

The current and the

voltage are said to be in 1010


11/56



WHAT ISINDUCTOR?????

1111


12/56


INDUCTOR

An inductor or a is a passive electrical component that

can store energy in a magnetic field created by the

electric current passing through it.

An inductor's ability to store magnetic energy is

measured by its inductance, in units of henries. Typically

an inductor is a conducting wire shaped as a coil; the loops

help to create a strong magnetic field inside the coil dueto Ampere's Law.

Due to the time-varying magnetic field inside the coil, a

voltage is induced, according to

Faraday's law of electromagnetic induction, which by1212
http://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Passivity_(engineering)http://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Henry_(unit)http://en.wikipedia.org/wiki/Ampere's_Lawhttp://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Ampere's_Lawhttp://en.wikipedia.org/wiki/Henry_(unit)http://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Electronic_componenthttp://en.wikipedia.org/wiki/Passivity_(engineering)


13/56


(CONTD)

Inductors are one of the basic components used in

electronics where current and voltage change with time,

due to the ability of inductors to delay and reshape

alternating currents.

Inductors called chokes are used as parts of filters inpower supplies or to block AC signals from passing

through a circuit.

The effective resistance of a coil in an AC circuit iscalled its inductive reactanceand is given by

XL = 2 L

When is in Hz and L is in H, XL will be in ohms 1313


14/56


INDUCTORS

1414


15/56



BEHAVIOR OF AC CIRCUITOF R-L SERIES

CIRCUIT!!!!!

1515

I UIT DIA AM


16/56


I UIT DIA AMPHASOR DIAGRAMS &

EQUATIONS

1616

WAVEFORMS


17/56


WAVEFORMS

Consider an AC circuit

with a source and an

inductor

The current in the

circuit is impeded bythe back EMF of the

inductor

The voltage across theinductor always leads

the current by 90

1717


18/56



WHAT ISCAPACITOR?????

1818


19/56


CAPACITORS

A basic capacitor has two parallel plates separated

by an insulating material

A capacitor stores an electrical charge betweenthe two plates

The unit of capacitance is Farads (F)

Capacitance values are normally smaller, such as

F, nF or pF

1919


20/56


(CONTD...)

Basic capacitor construction

2020

Dielectric

material

Plate

1

Plate2

The dielectric

material is aninsulator

therefore no

current flows

through the

capacitor


21/56


(CONTD...)

The function of capacitor is toStoring a charge between theplates

Electrons on the left plate

are attracted toward thepositive terminal of thevoltage source

This leaves an excess ofpositively charged holes

The electrons are pushedtoward the right plate

Excess electrons leave a

negative charge 2121

+ -

+_

+ _


22/56


CAPACITOR

2222


23/56



BEHAVIOR OF AC CIRCUITOF R-C SERIES

CIRCUIT!!!!!

2323


24/56


CIRCUITConsider a circuit containing a capacitor and an AC source

The current starts out at a large value and charges the plates of the

capacitor

There is initially no resistance to hinder the flow of the current

while the plates are not chargedAs the charge on the plates increases, the voltage across the plates

increases and the current flowing in the circuit decreases

The impeding effect of a capacitor on the current in an AC circuit is

called the capacitive reactanceand is given by

2424

C2

1

XC =


25/56


PHASOR DIAGRAMS

& EQUATIONS

2525


26/56


CAPACITORS IN AN AC

CIRCUITThe current reversesdirection

The voltage across theplates decreases as theplates lose the chargethey had accumulated

The voltage across thecapacitor lags behindthe current by 90

2626


27/56


ELEMENTS, IMPEDANCE

AND PHASE ANGLES

2727


28/56



BEHAVIOR OF AC CIRCUITOF R-L-C SERIES

CIRCUIT!!!!!

2828


29/56


CIRCUIT

The resistor, inductor,

and capacitor can be

combined in a circuitThe current in the

circuit is the same at

any time and varies

sinusoidally with time

2929


30/56


RELATIONSHIPS IN AN RLC

CIRCUITThe instantaneous voltage

across the resistor is inphase with the current

The instantaneous voltageacross the inductor leadsthe current by 90

The instantaneous voltageacross the capacitor lagsthe current by 90

3030

PHASOR DIAGRAMS


31/56


PHASOR DIAGRAMS

To account for the

different phases of

the voltage drops,vector techniques are

used

Represent the voltage

across each element asa rotating vector,

called a phasor

The diagram is called a 3131

PHASOR DIAGRAMS


32/56



PHASOR DIAGRAMS

3232

Vp

Ip

t

Vp

Ip

t

Vp

Ip

t

Resistor Capacitor Inductor

A phasor is an arrow whose length represents the

amplitude of an AC voltage or current.

The phasor rotates counterclockwise about the origin

with the angular frequency of the AC quantity.

Phasor diagrams are useful in solving complex ACcircuits.


33/56



-DIAGRAMS

3333

Vp

Ip

t

Vp

Ip

t

Vp

Ip

t

Resistor Capacitor Inductor


34/56


RS

From these equations, we can draw thephasor diagram to the right.

Assume:

imR

im

L

im

C

m

LC

R

Given: = m tsin

i i tm= sin( )

Qi

tm=

cos( )

di

dti tm= cos( )

V Ri Ri tR m= = sin( )

V Ldi

dtLi tL m= = cos( )

V

Q

C C i tC m= =

1

cos( )

l This picture corresponds to a snapshot att=0.The projections of these phasors alongthe vertical axis are the actual values of thevoltages at the given time.


35/56



Impedance of an AC Circuit

3535

R

L

C~

The impedance, Z, of a circuitrelates peakcurrent to peak voltage:

I VZ

pp= (Units:

OHMS)

(This is the AC equivalent of

Ohms law.)


36/56


Impedance of an RLC Circuit

R

L

C~E

As in DC circuits, we can use the loopmethod:

E - VR - VC - VL = 0I is same through all

components.

3636


37/56




3737

R

L

C~E

As in DC circuits, we can use the loopmethod:

E - VR - VC - VL = 0I is same through all

components.BUT: Voltages have differentPHASES

they add as PHASORS.


38/56




3838

Solve for thecurrent:

Ip = Vp

R2 + (Xc XL )2= Vp

Z

R

L

C~

d f C Ci i


39/56




3939

Solve for thecurrent:

Impedance:

Ip = Vp

R2 + (Xc XL )2= Vp

Z

Z= R2 +1

CL

2

R

L

C~

I d f RLC Ci i


40/56



The circuit hits resonance when 1/C-L=0: r=1/When this happens the capacitor and inductorcancel each otherand the circuit behaves purely resistively: IP=VP/R.


4040

Ip =Vp

Z

Z= R2 +1

C L

2

The currents magnitudedepends onthe driving frequency. When Zis a

minimum, the current is amaximum.This happens at a resonancefrequency:

LC

The current diesawayat both low and

high

IP

0

1 0

2

1 0

3

1 0

4

1 0

5

R = 1 0 0

R = 1 0

r

L=1mHC=10F

PHASOR DIAGRAM FOR


41/56


PHASOR DIAGRAM FORRLC SERIES CIRCUIT

The voltage across theresistor is on the +x axissince it is in phase withthe current

The voltage across theinductor is on the +ysince it leads the currentby 90

The voltage across thecapacitor is on the yaxis since it lags behind

the current by 90 4141


42/56


(CONTD)

The phasors are addedas vectors to account

for the phase

differences in the

voltages

VL and VC are on

the same line and so

the net y component isVL - VC

4242

asors or a er es


43/56



asors or a er esCircuit

4343

I

pVRp

(VCp-VLp)

VP

VCp

VLp

asors or a er es


44/56




4444

By Pythagoras theorem:(VP )2 = [ (VRp )2 + (VCp- VLp)2 ]

I

pVRp

(VCp-VLp)

VP

VCp

VLp

asors or a er es


45/56




4545

By Pythagoras theorem:(VP )2 = [ (VRp )2 + (VCp- VLp)2 ]

= -

I

pVRp

(VCp-VLp)

VP

VCp

VLp

Phase in an RLC Circuit


46/56



Phase in an RLC Circuit

4646

I

pVRp

(VCp-VLp)

V

P

VCp

VLp

We can also find the

phase:

tan = (VCp -VLp)/ VRp

or;tan = (XC-XL)/R.

or

tan = (1/C -

L) / R


47/56

Power in an AC


48/56



Power in an ACCircuit

V(t) = VP sin(t)I(t) = IP sin

(t)

P(t) = IV = IP VP sin

2(t)Note this oscillates

twice as fast.

V

t

2I

2

P

=0

(This is for apurely resistivecircuit.)

4848

Power in an AC


49/56



The power is P=IV. Since both I and V vary

in time, sodoes the power: P is a function of time.


Use, V = VP sin (t) and I = IP sin ( t+ ) :

P(t) = IpVpsin(t) sin ( t+ )

This wiggles in time, usually very fast. Whatwe usually

care about is the time average of this:P

TP t dt

T=

10

( ) (T=1/f)

4949

Power in an AC


50/56




Now: sin( ) sin( )cos cos( ) sin t t t+ = +

5050

Power in an AC


51/56




P t I V t t I V t t t

P P

P P

( ) sin( ) sin( ) sin ( )cos sin( )cos( ) sin

= += +

2


5151

Power in an AC


52/56





P P

P P


= += +

2

sin ( )

sin( ) cos( )

2 1

2

0

t

t t

=

=

Use:

and:So P I V P P=1

2cos


5252

Power in an AC


53/56





P P

P P


= += +

2

sin ( )

sin( ) cos( )

2 1

2

0

t

t t

=

=

Use:

and:So P I V P P=1

2cos

Now:

which we usually

write as

P I V rms rms= cos

sin( ) sin( )cos cos( ) sin t t t+ = +

5353

Power in an AC


54/56




P I V rms rms= cos( goes from -900 to 900, so the averagepower is positive)

cos() is called thepower factor.

For a purely resistive circuit the power factoris 1.

When R=0, cos()=0 (energy is traded butnot dissipated).Usually the power factor depends on

frequency. 5454

Power in an AC


55/56




P I V rms rms= cosWhat if f is not zero?I

V PHere I and V are 900

out of phase. (f=

900)

(It is purely reactive)

The time averageof

P is zero.

t

5555

O


56/56

POWERThe phase f between the current and the driving emf depends on the

relative magnitudes of the inductive and capacitive reactances.

R

XL

XC

tan = X XR

L CiZ

mm= X LL

XC

C 1

XL > XC > 0current

R

XL

XC

XL < XC < 0current

XL = XC = 0current

R

XL

XC

alternating current r-l-c series circuits

Documents