Alternating Current Theory 5/ Resonance

Physics Helpline
L K Satapathy
Alternating Current Theory 5
Resonance in LCR Series Circuit

Physics Helpline
L K Satapathy
Cells in Parallel
Resonance in LCR series circuit
2
2
. . . (1)
1
o o
o
E E
i
Z
R L
C


 
 
  
 
Current amplitude & voltage amplitude are related as
1 1
0o o
o
L
C LC
 

   
. . . (2)m o
o
E
i
R
 Maximum current amplitude is
It is maximum when frequency of AC
such that
o 
[Derived in AC Theory 4]
The variation of Io with  is shown in the figure
Each curve corresponds to a particular value of R
We observe that the value of decreases as R increasesm
oi

oi
o
1R
2R
3R
 1 2 3R R R 
1( )m
oi
2( )m
oi
3( )m
oi

Physics Helpline
L K Satapathy
Cells in Parallel
Let current amplitude for some value of  be
. . . (3)
2 2
m
o o
o
i E
i
R
 
 Power of the circuit becomes half the maximum power
We have two such frequencies symmetric about1 2&  o
1
2&
o
o
where   
  
  
  
 Half power band width 1 2 2    
oi
m
oi
12
m
oi
2
2 

Physics Helpline
L K Satapathy
Cells in Parallel
1 2
2
1
1
, . . . (4)
1
o
o
E
For i
R L
C
 


 
 
  
 
2
2
1
1
(3) & (4)
21
o oE E
R
R L
C


 
 
  
 
2
2
1
1
1
2R L R
C


 
    
 
2
2 2
1
1
1
2R L R
C


 
    
 

Physics Helpline
L K Satapathy
Cells in Parallel
2
2
1
1
1
L R
C


 
   
 
1
1
1
L R
C


  
1
( )
( )
o
o
L R
C
 
 
    
 
1
1
1
o
o
o
o
L R
C


 


 
    
    
 

Physics Helpline
L K Satapathy
Cells in Parallel
1
1
o
o
o
o
L
L R


 

 
    
    
 
1
o
o
L
C


 
 
 

1
1 1o o
o o
L L R
 
 
 

    
       
   
1 1o o
o o
L L R
 
 
 
    
       
   
1
o





 
 
2
o
o
L R




  
2 [ ]Bandwid
R
L
th  

Physics Helpline
L K Satapathy
Cells in Parallel
1
2
o o
o
L
Q
R CR
 
 
  

We define Quality factor
 When the value of Q is larger
Band width 2 is smaller
Resonance is sharper
The circuit will be more selective
2 o
Q

  
This phenomenon is used in Radio Tuners

Physics Helpline
L K Satapathy
For More details:
www.physics-helpline.com
Subscribe our channel:
youtube.com/physics-helpline
Follow us on Facebook and Twitter:
facebook.com/physics-helpline
twitter.com/physics-helpline

Alternating Current Theory 5/ Resonance

More Related Content

What's hot (20)

Viewers also liked (13)

Similar to Alternating Current Theory 5/ Resonance (20)

More from Lakshmikanta Satapathy (18)

Recently uploaded (20)

Alternating Current Theory 5/ Resonance