Alternating Current PPT Physics Class 12

 Page 1


ALTERNATING  CURRENTS
1. Alternating EMF and Current 
2. Average or Mean Value of Alternating EMF and Current
3. Root Mean Square Value of Alternating EMF and Current
4. A C Circuit with Resistor
5. A C Circuit with Inductor
6. A C Circuit with Capacitor
7. A C Circuit with Series LCR – Resonance and Q-Factor
8. Graphical Relation between Frequency vs X
L
, X
C
9. Power in LCR  A C Circuit
10.Watt-less Current
11.L C Oscillations
12.Transformer
13.A.C. Generator
Page 2


ALTERNATING  CURRENTS
1. Alternating EMF and Current 
2. Average or Mean Value of Alternating EMF and Current
3. Root Mean Square Value of Alternating EMF and Current
4. A C Circuit with Resistor
5. A C Circuit with Inductor
6. A C Circuit with Capacitor
7. A C Circuit with Series LCR – Resonance and Q-Factor
8. Graphical Relation between Frequency vs X
L
, X
C
9. Power in LCR  A C Circuit
10.Watt-less Current
11.L C Oscillations
12.Transformer
13.A.C. Generator
Alternating emf:
Alternating emf is that emf  which continuously changes in magnitude and 
periodically reverses its direction.
Alternating Current:
Alternating current is that current  which continuously changes in magnitude 
and periodically reverses its direction.
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
sin ?t
I  = I
0
sin ?t
E, I – Instantaneous value of emf and current 
E
0
, I
0
– Peak or maximum value or amplitude of emf and current
? – Angular frequency          t – Instantaneous time
?t – Phase
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
cos ?t
I  = I
0
cos ?t
Symbol of 
AC Source
Page 3


ALTERNATING  CURRENTS
1. Alternating EMF and Current 
2. Average or Mean Value of Alternating EMF and Current
3. Root Mean Square Value of Alternating EMF and Current
4. A C Circuit with Resistor
5. A C Circuit with Inductor
6. A C Circuit with Capacitor
7. A C Circuit with Series LCR – Resonance and Q-Factor
8. Graphical Relation between Frequency vs X
L
, X
C
9. Power in LCR  A C Circuit
10.Watt-less Current
11.L C Oscillations
12.Transformer
13.A.C. Generator
Alternating emf:
Alternating emf is that emf  which continuously changes in magnitude and 
periodically reverses its direction.
Alternating Current:
Alternating current is that current  which continuously changes in magnitude 
and periodically reverses its direction.
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
sin ?t
I  = I
0
sin ?t
E, I – Instantaneous value of emf and current 
E
0
, I
0
– Peak or maximum value or amplitude of emf and current
? – Angular frequency          t – Instantaneous time
?t – Phase
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
cos ?t
I  = I
0
cos ?t
Symbol of 
AC Source
Average or Mean Value of Alternating Current:
Average or Mean value of alternating current over half cycle is that steady 
current which will send the same amount of charge in a circuit in the time of 
half cycle as is sent by the given alternating current in the same circuit in 
the same time.
dq = I dt = I
0 
sin ?t dt
q = ? I
0
sin ?t dt
0
T/2
q = 2 I
0
/ ? =   2 I
0
T / 2p =   I
0
T / p
Mean Value of AC,     I
m
= I
av  
=   q / (T/2)
I
m
= I
av   
=  2 I
0
/ p =  0.637 I
0
=  63.7 % I
0
Average or Mean Value of Alternating emf:
E
m
= E
av   
=  2 E
0
/ p =  0.637 E
0
=  63.7 % 
E
0
Note: Average or Mean value of alternating current or emf is zero over a 
cycle as the + ve and – ve values get cancelled. 
Page 4


ALTERNATING  CURRENTS
1. Alternating EMF and Current 
2. Average or Mean Value of Alternating EMF and Current
3. Root Mean Square Value of Alternating EMF and Current
4. A C Circuit with Resistor
5. A C Circuit with Inductor
6. A C Circuit with Capacitor
7. A C Circuit with Series LCR – Resonance and Q-Factor
8. Graphical Relation between Frequency vs X
L
, X
C
9. Power in LCR  A C Circuit
10.Watt-less Current
11.L C Oscillations
12.Transformer
13.A.C. Generator
Alternating emf:
Alternating emf is that emf  which continuously changes in magnitude and 
periodically reverses its direction.
Alternating Current:
Alternating current is that current  which continuously changes in magnitude 
and periodically reverses its direction.
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
sin ?t
I  = I
0
sin ?t
E, I – Instantaneous value of emf and current 
E
0
, I
0
– Peak or maximum value or amplitude of emf and current
? – Angular frequency          t – Instantaneous time
?t – Phase
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
cos ?t
I  = I
0
cos ?t
Symbol of 
AC Source
Average or Mean Value of Alternating Current:
Average or Mean value of alternating current over half cycle is that steady 
current which will send the same amount of charge in a circuit in the time of 
half cycle as is sent by the given alternating current in the same circuit in 
the same time.
dq = I dt = I
0 
sin ?t dt
q = ? I
0
sin ?t dt
0
T/2
q = 2 I
0
/ ? =   2 I
0
T / 2p =   I
0
T / p
Mean Value of AC,     I
m
= I
av  
=   q / (T/2)
I
m
= I
av   
=  2 I
0
/ p =  0.637 I
0
=  63.7 % I
0
Average or Mean Value of Alternating emf:
E
m
= E
av   
=  2 E
0
/ p =  0.637 E
0
=  63.7 % 
E
0
Note: Average or Mean value of alternating current or emf is zero over a 
cycle as the + ve and – ve values get cancelled. 
Root Mean Square or Virtual or Effective Value of 
Alternating Current:
Root  Mean Square (rms) value of alternating current is that steady current 
which would produce the same heat in a given resistance in a given time as 
is produced by the given alternating current in the same resistance in the 
same time.
dH = I
2
R dt = I
0
2
R sin
2
?t dt
H = ? I
0
2
R sin
2
?t dt
0
T
H = I
0
2
RT / 2
If I
v
be the virtual value of AC,    then
I
v
= I
rms   
= I
eff
= I
0
/ v2 =  0.707 I
0
=  70.7 % I
0
Root Mean Square or Virtual or Effective Value of 
Alternating emf:
E
v
= E
rms   
= E
eff
=  E
0
/ v2 = 0.707 E
0
= 70.7 % E
0
Note:
1.  Root  Mean Square value of alternating current or emf can be calculated over  any 
period of the cycle since it is based on the heat energy produced.
2.  Do not use the above formulae if the time interval under the consideration is less than 
one period.
(After integration, ? is replaced with 2 p / T)
H = I
v
2
RT
Page 5


ALTERNATING  CURRENTS
1. Alternating EMF and Current 
2. Average or Mean Value of Alternating EMF and Current
3. Root Mean Square Value of Alternating EMF and Current
4. A C Circuit with Resistor
5. A C Circuit with Inductor
6. A C Circuit with Capacitor
7. A C Circuit with Series LCR – Resonance and Q-Factor
8. Graphical Relation between Frequency vs X
L
, X
C
9. Power in LCR  A C Circuit
10.Watt-less Current
11.L C Oscillations
12.Transformer
13.A.C. Generator
Alternating emf:
Alternating emf is that emf  which continuously changes in magnitude and 
periodically reverses its direction.
Alternating Current:
Alternating current is that current  which continuously changes in magnitude 
and periodically reverses its direction.
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
sin ?t
I  = I
0
sin ?t
E, I – Instantaneous value of emf and current 
E
0
, I
0
– Peak or maximum value or amplitude of emf and current
? – Angular frequency          t – Instantaneous time
?t – Phase
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
0
p 2p 3p 4p p/2 3p/2 5p/2 7p/2 ? = ?t
E 
,I
E
0
I
0
E = E
0
cos ?t
I  = I
0
cos ?t
Symbol of 
AC Source
Average or Mean Value of Alternating Current:
Average or Mean value of alternating current over half cycle is that steady 
current which will send the same amount of charge in a circuit in the time of 
half cycle as is sent by the given alternating current in the same circuit in 
the same time.
dq = I dt = I
0 
sin ?t dt
q = ? I
0
sin ?t dt
0
T/2
q = 2 I
0
/ ? =   2 I
0
T / 2p =   I
0
T / p
Mean Value of AC,     I
m
= I
av  
=   q / (T/2)
I
m
= I
av   
=  2 I
0
/ p =  0.637 I
0
=  63.7 % I
0
Average or Mean Value of Alternating emf:
E
m
= E
av   
=  2 E
0
/ p =  0.637 E
0
=  63.7 % 
E
0
Note: Average or Mean value of alternating current or emf is zero over a 
cycle as the + ve and – ve values get cancelled. 
Root Mean Square or Virtual or Effective Value of 
Alternating Current:
Root  Mean Square (rms) value of alternating current is that steady current 
which would produce the same heat in a given resistance in a given time as 
is produced by the given alternating current in the same resistance in the 
same time.
dH = I
2
R dt = I
0
2
R sin
2
?t dt
H = ? I
0
2
R sin
2
?t dt
0
T
H = I
0
2
RT / 2
If I
v
be the virtual value of AC,    then
I
v
= I
rms   
= I
eff
= I
0
/ v2 =  0.707 I
0
=  70.7 % I
0
Root Mean Square or Virtual or Effective Value of 
Alternating emf:
E
v
= E
rms   
= E
eff
=  E
0
/ v2 = 0.707 E
0
= 70.7 % E
0
Note:
1.  Root  Mean Square value of alternating current or emf can be calculated over  any 
period of the cycle since it is based on the heat energy produced.
2.  Do not use the above formulae if the time interval under the consideration is less than 
one period.
(After integration, ? is replaced with 2 p / T)
H = I
v
2
RT
0
p 2p 3p 4p
T/4    T/2    3T/4    T    5T/4  3T/2   7T/4  2T
t
p/2 3p/2 5p/2 7p/2 ? = ?t
E
0
E
v
E
m
Relative Values Peak, 
Virtual and Mean Values of 
Alternating emf:
E
m
= E
av   
=  0.637 E
0
E
v
= E
rms   
= E
eff
= 0.707 
E
0
Tips:
1. The given values of alternating emf and current are virtual values unless 
otherwise specified.
i.e. 230 V AC means  E
v
=  E
rms
=  E
eff 
= 230 V
2. AC Ammeter and AC Voltmeter read the rms values of alternating current 
and voltage respectively.
They are called as ‘hot wire meters’.
3.   The scale of DC meters is linearly graduated where as the scale of AC 
meters is not evenly graduated because H  a I
2