Important Formulas: Alternating Current | Physics Class 12 - NEET PDF Download

 Page 1


ALTERNATING CURRENT
1. AC AND DC CURRENT :
A current that changes its direction periodically is called alternating cur-
rent (AC). If a current maintains its direction constant it is called direct
current (DC).
3. ROOT MEAN SQUARE VALUE:
Root Mean Square Value of a function, from t
1
 to t
2
, is defined as
f
rms
 = 
1 2
2
2
1
t t
dt f
t
t
?
?
 .
4. POWER CONSUMED OR SUPPLIED IN AN AC CIRCUIT:
Average power consumed in a cycle  = 
?
?
?
?
?
2
2
o
Pdt
=
2
1
 V
m
 ?
m
 cos ?
= 
2
V
m
 . 
2
m
?
 . cos ? = V
rms
 ?
rms
 cos ?.
Here cos ? ? is called power factor.
Page 2


ALTERNATING CURRENT
1. AC AND DC CURRENT :
A current that changes its direction periodically is called alternating cur-
rent (AC). If a current maintains its direction constant it is called direct
current (DC).
3. ROOT MEAN SQUARE VALUE:
Root Mean Square Value of a function, from t
1
 to t
2
, is defined as
f
rms
 = 
1 2
2
2
1
t t
dt f
t
t
?
?
 .
4. POWER CONSUMED OR SUPPLIED IN AN AC CIRCUIT:
Average power consumed in a cycle  = 
?
?
?
?
?
2
2
o
Pdt
=
2
1
 V
m
 ?
m
 cos ?
= 
2
V
m
 . 
2
m
?
 . cos ? = V
rms
 ?
rms
 cos ?.
Here cos ? ? is called power factor.
5. SOME DEFINITIONS:
The factor cos ? is called Power factor.
?
m
 sin ? is called wattless current.
Impedance Z is defined as Z = 
m
m
V
?
 = 
rms
rms
V
?
?L is called inductive reactance and is denoted by X
L.
C ?
1
 is called capacitive reactance and is denoted by X
C.
6. PURELY RESISTIVE CIRCUIT:
I =
R
s
v
=
R
t sin V
m
?
= ?
m
 sin ?t
?
m 
= 
R
V
m
?
rms
 = 
R
V
rms
<P> = V
rms
?
rms
cos ? ? ? ?
R
V
rms
2
7. PURELY CAPACITIVE CIRCUIT:
I =  =
C
1
V
m
?
cos ?t
= 
C
m
X
V
cos ?t = ?
m
 cos ?t.
X
C
 = 
C
1
?
 and is called capacitive reactance.
V
t
v
T
t
I
i
Page 3


ALTERNATING CURRENT
1. AC AND DC CURRENT :
A current that changes its direction periodically is called alternating cur-
rent (AC). If a current maintains its direction constant it is called direct
current (DC).
3. ROOT MEAN SQUARE VALUE:
Root Mean Square Value of a function, from t
1
 to t
2
, is defined as
f
rms
 = 
1 2
2
2
1
t t
dt f
t
t
?
?
 .
4. POWER CONSUMED OR SUPPLIED IN AN AC CIRCUIT:
Average power consumed in a cycle  = 
?
?
?
?
?
2
2
o
Pdt
=
2
1
 V
m
 ?
m
 cos ?
= 
2
V
m
 . 
2
m
?
 . cos ? = V
rms
 ?
rms
 cos ?.
Here cos ? ? is called power factor.
5. SOME DEFINITIONS:
The factor cos ? is called Power factor.
?
m
 sin ? is called wattless current.
Impedance Z is defined as Z = 
m
m
V
?
 = 
rms
rms
V
?
?L is called inductive reactance and is denoted by X
L.
C ?
1
 is called capacitive reactance and is denoted by X
C.
6. PURELY RESISTIVE CIRCUIT:
I =
R
s
v
=
R
t sin V
m
?
= ?
m
 sin ?t
?
m 
= 
R
V
m
?
rms
 = 
R
V
rms
<P> = V
rms
?
rms
cos ? ? ? ?
R
V
rms
2
7. PURELY CAPACITIVE CIRCUIT:
I =  =
C
1
V
m
?
cos ?t
= 
C
m
X
V
cos ?t = ?
m
 cos ?t.
X
C
 = 
C
1
?
 and is called capacitive reactance.
V
t
v
T
t
I
i
I
C
 leads by v
C
 by ?/2 Diagrammatically
(phasor diagram) it is represented as
?
m
V
m
.
Since ? ? ? ??º,  <P> = V
rms
 ?
rms
cos ? ? ? ? ?