REACTANCE, RESONANCE

1
REACTANCE, RESONANCE PHASE ANGLE When an A.C.
is applied to pure resistors, inductors and
capacitors, we see some interesting effects.
WAVE FORMS
PHASE DIAGRAM
CCT
IL
VC
IC
?C
2
FOR A.C. CIRCUITS In a purely resistive CCT, ir
and ?r are in phase. In a purely inductive CCT,
iL lags ?L by 90o In a purely capacitive CCT, iL
leads ?C by 90o Both capacitors and inductors
have a property similar to resistance called
Reactance (X) and is measured in Ohms. XL 2TT
? L OHMS XC 1 OHMS
2TT? L OHMS
3

Remember, iL is common to both RL. It follows
that ?R I are in phase and ?L leads both by
90o
? is the applied voltage. It is the Phasor Sum
of ?r ?r
Using Pythagoras Theorem
4

If ?r ?L are out of phase and, from Ohms law,
current is dependent on voltage and a constant
which opposes current flow, it follows that XL
R are related by a phasor sum. In A.C. circuits
impedance is the phasor sum of XL R. One
way to remember how to find Z ?, is
Ohms
Ohms
?LiXL
?iZ
Z
XL
R
?riR
5
Similar results are found in RC
CCTs R, L, C Circuits
?r is in phase with I ?L leads I
by 90o ?c lags I by 90O To find
? we have to know the difference between ?L and
?C
?ciXc
i
?L
?r
?c
?
6
Depending on ?, L C, XL can be greater than Xc
or vice versa.
?L iXL
i
?R iR
?C iXL
If ?L gt ?C
If ?L gt ?C
?r
?
?
(?L-?C)
(?L-?C)
?
?
?R
7

• RESONANCE
• When XC XL A R,L,C CCT is said to be
  resonant.
• i) The applied voltage and the current are in
  phase.
• ii) Z R i.e. the minimum 2/
• iii) i ?/R i.e. maximum current
• iv) XL - 2? ?L XC ½??C
• ? 2? ?L ½??C
• ? HZ
• At ?o, if R ? XC XL it is possible for ?c ?L
  to be many times greater than the supply voltage.
• Voltage magnification ?L(or Vc)
• Q
  ?

8
COMMENT Resonant CCTs can have very high
voltages so be careful. Do not Poke Prod
series RLC CCTs! Resonance has many practical
uses in filtering out unwanted frequencies e.g. a
radio. Aerial receives all frequencies. L
is fixed but C can be varied. AT resonance, the
voltage from the aerial is magnified many times.
The amplified voltage drives the headphones.
Crystal Radio Set