biology chapter 4 form 4

8/18/2019 biology chapter 4 form 4

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4.0

RESONANCE

BAKISS HIYANA BT ABU BAKAR

JKE,POLISAS

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COURSE LEARNING OUTCOME

1. Explain AC circuit concept and their

analysis using AC circuit law.

2. Apply the knowledge of AC circuit in solving

problem related to AC electrical circuit.

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4.1 UNDERSTAND

RESONANCE IN SERIES ANDPARALLEL CIRCUITS


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SERIES RESONANCE:

Current will be maximum offering minimum

impedance.


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RESONANCE FUNCTIONS:

!esonance circuit serves as stable fre#uencysource.

!esonance circuit serves as filter.

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5he fre#uency set by the tank

circuit is solely dependent

upon the value of " C

Acting as a short

of fre#uency6filter7 to strain

certain

fre#uencies out

of a mix ofothers


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4.1.2 EXPLAIN THE EFFECT OF CHANGING

THE FREQUENCY TO

A! RLC SERIES CIRCUIT:

A series !"C circuit8s reactance changes as

you change the voltage source8s fre#uency. 9ts total impedance also changes.

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At low fre#uencies$ /c ; /" and the circuit is

primarily capacitive. At high fre#uencies$ /" ; /c and the circuit is

primarily inductive.

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B! RLC PARALLEL CIRCUIT:

!eactance change as you change the voltagesource8s fre#uency.

At low fre#uencies$ /" < /c and the circuit is

primarily inductive.

At high fre#uencies$ /c< /" and the circuit isprimarily capacitive.

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4.1." DRA# THE GRAPH OF IMPEDANCE $S

FREQUENCY

SERIES:

A series !"C circuit contains both inductive reactance )/"* andcapacitive reactance )/c*.

=ince /" and /c have opposite phase angles$ they tend to cancel

each other out and the circuit8s total reactance is smaller that

either individual reactance,

/5 < /" /5 < /c 12


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PARALLEL:

5he smaller reactance dominates$ since a smaller

reactance results in a larger branch current.

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4.1.4 PRODUCE RESONANT FREQUENCY

EQUATION FOR SERIES CIRCUITS

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4.1.& DETERMINE:

)a* > factor,

( > is the ratio of power stored to power dissipated in the circuit

reactance and resistance.

( > is the ratio of its resonant fre#uency to its bandwidth.

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=E!9E= C9!C?95,

9@+


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A!A""E" C9!C?95,

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)a* >uality factor, the ratio of the circulating branch currents to the supply

current .


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)b* @re#uency bandwidth$ B & f2 f1,

Bandwidth$ Df is measured between the -. amplitude points of

series resonant circuit.

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5he difference between the two halfFpower fre#uencies.


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"ower cutFoff fre#uency$ )G "*,

?pper cutFoff fre#uency$ )G H*,

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A HIGH Q RESONANT CIRCUIT HAS A NARROW BANDWIDTH AS

COMPARED TO A LOW Q

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BI & f cJ>Ihere,

f c & resonant fr#uency

> & #uality factor


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A LO# Q DUE TO A HIGH RESISTANCE IN SERIES #ITH THE

INDUCTOR PRODUCES A LO# PEAK ON A BROAD RESPONSE

CUR$E FOR A PARALLEL RESONANT CIRCUIT

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Parallel resonant response varies with Q.


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EXAMPLE:

In Figure above, the 100% current point is 50 mA. The 70.7% level is 0707(50

mA)!5." mA.

The upper an# lo$er ban# e#ges rea# rom the curve are &'1 or l an# !55

or h. The ban#$i#th is *" , an# the hal po$er points are + !& o the center

resonant reuenc- / h l !55&'1 *"

l c 2& !&!!& &'1

h c 3 2& !&!3!& !55

4ince / c26

c2/ (!&! )2(*" ) 522


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)c* 5he dissipation factor$ K, 5he ratio of the power loss in a dielectric material to the total

power transmitted through the dielectric.

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SUMMARY OF THE CHARACTERISTICS OF

RESONANT RLC CIRCUITS:

CHARACTERISTIC SERIES CIRCUIT PARALLEL CIRCUIT

!esonant fre#uency$fr

>uality factor$>

Bandwidth$ BI

Half powerfre#uency$f " f H

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EXAMPLE NO1

A series resonance network consisting of a resistor of 3-L$ a capacitor

of 2u@ and an inductor of 2-mH is connected across a sinusoidal supplyvoltage which has a constant output of : volts at all fre#uencies.

Calculate$ the resonant fre#uency$ the current at resonance$ the

voltage across the inductor and capacitor at resonance$ the #uality

factor and the bandwidth of the circuit. Also sketch the corresponding

current waveform for all fre#uencies.

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SOLUTION

!esonant @re#uency$ G r

Circuit Current at !esonance$ 9m

9nductive !eactance at !esonance$ /"

Moltages across the inductor and the

capacitor$ M"$ MC

Bandwidth$ BI

5he upper and lower F3dB fre#uency

points$ G H and G "

Current Iaveform

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EXAMPLE NO2

A series circuit consists of a resistance of L$ an inductance of --mH and

a variable capacitance connected across a 1--M$ -HN supply. Calculate

the capacitance re#uire to give series resonance and the voltagesgenerated across both the inductor and the capacitor.

=olution,


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Moltages across the inductor and the capacitor$ M"$ MC


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EXAMPLE NO"

A parallel resonance network consisting of a resistor of -L$ a capacitor of

12-u@ and an inductor of 2--mH is connected across a sinusoidal supplyvoltage which has a constant output of 1-- volts at all fre#uencies.

Calculate$ the resonant fre#uency$ the #uality factor and the bandwidth of

the circuit$ the circuit current at resonance and current magnification.

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SOLUTION:


9nductive !eactance at !esonance$

/"

>uality factor$ >

Bandwidth$ BI

5he upper and lower F3dB fre#uency

points$ G H and G "

Circuit Current at !esonance$ 95

At resonance the dynamic impedance

of the circuit is e#ual to !

Current Oagnification$ 9mag

Ie can check this value by

calculating the current flowing

through the inductor )or capacitor*

at resonance.

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SUMMARY

@or resonance to occur in any circuit it must have at least

one inductor and one capacitor.

!esonance is the result of oscillations in a circuit as stored

energy is passed from the inductor to the capacitor.

!esonance occurs when /" & /C and the imaginary part of the

transfer function is Nero.

At resonance the impedance of the circuit is e#ual to the

resistance value as % & !.

biology chapter 4 form 4

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