Class 12 Physics Study Material on Alternating Current

In Class 12 Physics, students explore Alternating Current (AC), a fundamental concept in electrical engineering. Unlike Direct Current (DC), AC periodically reverses the flow of electric charge, generating sinusoidal waveforms. Topics include waveform representation, frequency, voltage, and current analysis. AC finds applications in power systems, electronics, and appliances. Through theory and experiments, students gain vital insights for future studies in electrical engineering.
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1. Alternating Current
·Alternating Current:
The current whose magnitude changes with time and direction reverses periodically is
called alternating current. a) Alternating emf E and current I at any time am given by:
0
sinE E tw=
Where
0
ENBAw=
0
sin()I I twf= -

Where
0
NBA
I
R
w
=
2
2n
T
p
w p
= =
Where T is the time period.
·Values of Alternating Current and Voltage a)Instantaneous value:
It is
the value of alternating current and voltage at an instant t.
b)Peak value:
Maximum values of voltage E
0 and current I0 in a cycle are called peak values.
c)Mean value:
For complete cycle,
0
0
1
0
1
0
T
T
E Edt
T
I Idt
T
<>= =
<>= =∫
∫
Mean value for half cycle:
0
2
mean
E
E
p
=
d) Root – mean- square (rms) value:
2 1 / 2 0
0 0
2 1 / 20
0 0
( ) 0.707 70.7%
2
( ) 0.707 70.7%
2
rms
rms
E
E E E E
I
I I I I
= < > = = =
= < > = = =
RMS values are also called apparent or effective values.
·Phase difference Between the EMF (Voltage) and the Current in an AC Circuit
a)For pure resistance:
The voltage and the current are in same phase i.e. phase difference
0f=
b)For pure inductance: $OOULJKWFRS\UHVHUYHG1RSDUWRIWKHPDWHULDOFDQEHSURGXFHGZLWKRXWSULRUSHUPLVVLRQ

2. The voltage is ahead of current by
2
p
i.e. phase difference
2
p
f
= +.
c)For pure capacitance:
The voltage lags behind the current by
2
p
i.e. phase difference
2
p
f
=-
·Reactance:
a)
0
0
Reactance
X = / 2
rms
rms
E EE
I I I
p= = ±
b)
Inductive reactance
X = L=2nL
L
wp

c)
Capacitive reactance
1 1
X =
2
C
C nCw p
=
·Impedance:
Impedance is defined as,
0
0
rms
rms
E EE
Z
I I I
f= = =
Where fis the phase difference of the voltage E relative to the current I.
a)For L – R series circuit:2 2 2 2
RL L
Z R X R L w= + = +
1
tan tan
L L
or
R R
w w
f f
-   
= =
   
   

b) For R – C series circuit:
2
2 2 2
1
RC C
Z R X R
C
w
 
= + = +
 
1
tan
CR
f
w= Or
11
tan
CR
f
w
- 
=
 
 

c) For L – C series circuit:
2 2
( )
LCR L C
Z R X X= + -
2
2
1
R Lw
w
C
 
= + -
 
 1
tan
L
C
Rw
w
f
 
-
 
 
= Or
1
1
tan
L
C
R
w
w
f
-
 
-
 
=  
 
 

·Conductance:
Reciprocal of resistance is called conductance. $OOULJKWFRS\UHVHUYHG1RSDUWRIWKHPDWHULDOFDQEHSURGXFHGZLWKRXWSULRUSHUPLVVLRQ

3. 1
G mho
R
=
·Power in and AC Circuit:
a)Electric power = (current in circuit) x (voltage in circuit)
P = IE
b) Instantaneous power:
P
inst = Einst x Iinst
c) Average power:
00
1
cos cos
2
av rmsrms
P E I E If f= =
d) Virtual power (apparent power):
00
1
2
rms rms
E I E I= =
·Power Factor: a)Power factor
cos
av
v
P
R
P Z
f==
b) For pure inductance
Power factor, cos=1 f
c) For pure capacitance
Power factor, cos=0 f
d) For LCR circuit
2
2
Power factor, cos=
1
R
R L
C f
w
w
 
+ -
 
 
1
X L
w
w
C
 
= -
 
 ·Wattless Current:
The component of current differing in phase by
2
p
relative to the voltage, is called
wattles current.
·The rms value of wattless current:
0
0
sin
2
sin
2
rms
I
I
X
I
Z
f
f=
 
= =
 

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4. ·Choke Coil:
a)An inductive coil used for controlling alternating current whose self- inductance is
high and resistance in negligible, is called choke coil.
b)The power factor of this coil is approximately zero.
·Series Resonant Circuit
a)When the inductive reactance (XL) becomes equal to the capacitive reactance (XC) in
the circuit, the total impedance becomes purely resistive (Z=R).
b)In this state, the voltage and current are in same phase (
f = 0), the current and
power are maximum and impedance is minimum. This state is called resonance.
c)At resonance,
1
r
r
L
Cw
w
=
Hence, resonance frequency is,
1
2
r
f
LC
p
=
d) In resonance, the power factor of the circuit is one.
·Half – Power Frequencies: Those frequencies f
1 and f2 at which the power is half of the maximum power (power at
resonance), i.e., f
1 and f2 are called half – power frequencies.ma x
ma x
m a x
1
2
2
2
P P
I
I
P
P
=
=
\=
·
Band – Width: a)The frequency interval between half – power frequencies is called band – width.
2 1
Bandwidth f = f f\ D -
b) For a series LCR resonant circuit,
1
f =
2
R
L
p
D
·
Quality Factor (Q):
( )
2 1
Maximum energy stored
2
Energy dissipated per cycle
2 Maximum energy stored
Mean power dissipated
1
r r r
r
Q
T
Or
L f f
Q
R CR f f fp
p
w
w= ´
= ´
= = = =
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