JEE Physics/ Lakshmikanta Satapathy/ Alternating Current Theory part 1/ Mean value of Alternating Current and its relation with Peak value discussed with the related concepts

1. Physics Helpline
L K Satapathy
Alternating Current Theory 1
Mean Value of AC
0 0
2
0.636mI I I

 

2. Physics Helpline
L K Satapathy
Cells in Parallel
Alternating Current Theory 1
Alternating Current :
Electric current whose magnitude changes
continuously and direction (polarity) reverses
periodically with time is known as Alternating
Current.
Alternating current which varies sinusoidally with time is given by
0 0
2
sin sinI I t I t
T

 
Peak value (Amplitude)0I 
  Angular frequency
Time periodT 
I
t
2
T0 T

3. Physics Helpline
L K Satapathy
Cells in Parallel
Alternating Current Theory 1
Mean value of AC : It is that value of steady current which will send the same
amount of charge through a resistor in a half cycle of AC as is sent by the
alternating current through the same resistor in the same time.
I
t
2
TO
1 2 3 n
2
T
t
n
 
1 2, , . . . , ni i i
1 1 2 2, , . . . , n nq i t q i t q i t  
1 2 1 2... ( . . . )n nq q q q i i i t       
Half cycle (T/2) of an AC is shown in the figure
Divide it into n equal time intervals (t)
Let the currents in these intervals be
 Charge sent in these intervals are
 Total charge sent in the half cycle is given by
1 2( . . . ) . . . (1)
2
n
T
q i i i
n
    

4. Physics Helpline
L K Satapathy
Cells in Parallel
Alternating Current Theory 1
I
t
2
TO
mI
1 2(1) & (2) ( . . . )
2 2
m
n
I T T
i i i
n
    
1 2 . . . n
m
i i i
I
n
  
 
Let the mean value of AC = Im
 Charge sent by it in time (T/2) is given by
. . . (2)
2
mI T
q 

5. Physics Helpline
L K Satapathy
Cells in Parallel
Alternating Current Theory 1
0 sin
dq
I I t
dt
 
 Charge sent by AC in time T/2 is
2
0
0
cos
T
t
I


 
  
 
0
[cos( 2) cos0]
I
T

  
0 sin .dq I t dt 
Relation between Mean value and Peak value of AC :
Instantaneous current
2
0
0
sin .
T
q I t dt 

6. Physics Helpline
L K Satapathy
Cells in Parallel
Alternating Current Theory 1
0
2
mI T I T

 
(2)
2
mI T
Also q 
2
2T
T

    
0
[cos cos0]
2
I
q
T


   
0
[ 1 1]
2
I
T
   
0 0
( 2)
2
I T I T
 
    
0 0 0
2 7
0.636
11
mI I I I

   

7. Physics Helpline
L K Satapathy
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