Class Notes Industrial Lec11
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Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
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Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
2 3 *+.4 ""
'
'.
# ) *+.4 52 50*+14 '( ( ) : ) 3 ;" 2 )$ 3 ;" 2 (.*+,% ) 3 ;" 2 4.*+,% ( ( ) : ) $3 ) ()$ 3 ;" 2 (;" 2 (.*+,% 3 ;"#. 2 (*+,%# *+,% 3 < ,;" *+.42 (*+,% 3 < ,;" 2 4*+1% )$ 3 )$ () 3 < ,;" 2 (*+.% ) 3 ) () = 3Vmsin( t+ /2) ) ) ": π / 2 +α 6 Vdc = v ab d (ωt ) 2π π / 6+α = = = = = =
'
"
Vn =
(--
3
π
π / 2 +α
" )
(6.
)
$
""
'.
# '1 ( (
)
)
#
3Vm sin(ωt + π / 6)d (ωt )
π / 6 +α
3 3Vm
[− cos(ωt + π / 6)]ππ // 26++αα
3 3Vm
[− cos(π / 2 + α + π / 6) + cos(π / 6 + α + π / 6)]
3 3Vm
[cos(π / 3 + α ) − cos(2π / 3 + α )]
π
π
π
3 3Vm
π
3 3Vm
π
.2 sin(π / 2 + α ) sin(π / 6) cos α
" =" " ) 3 3Vm Vdm =
'
'
'1
)
π
)
36
)
:
:
Vdc = cos α Vdm )
":
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
Vrms
π / 2+α
6 = 2π
1/ 2
3V sin (ωt + π / 6)d (ωt ) 2 m
2
π / 6 +α
3 3Vm2 = . π 2
1/ 2
π / 2 +α
(1 − cos(2ωt + π / 3))d (ωt )
π / 6 +α
9Vm2 sin( 2ωt + π / 3) ωt − = 2π 2 =
π / 2 +α
1/ 2
π / 6 +α
sin(π / 3 + 2α + π / 3) sin(π + 2α + π / 3) π /2 +α − −π / 6 −α + 2 2 2π
3Vm
3Vm π 1 = − {sin( 4π / 3 + 2α ) − sin(2π / 3 + 2α )} 2π 3 2 3Vm π 1 = − .2 cos(π + 2α ) sin(π / 3) 2π 3 2 3Vm π 3 cos 2α = + 2 2π 3
>?
(--
#!
= Vm = Vm
3 9 3 cos 2α + 2 4π
(6,
1/ 2
1/ 2
1/ 2
1 3 3 cos 2α + 2 4π )
1/ 2
1/ 2
9 π 9 3 . + . cos 2α 2π 3 2π 2
= 3Vm
1/ 2
1/ 2
@
""
7 #?
A
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
+. 44 T1
T3
T5
)8-
$
+. ( 4
) +. 4
) +. ( (
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+
8
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8
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+
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6
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,*+.
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) -
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.
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π
" -
# )
$ B ( ($ B # )
$ .
) (
) "
)
3 3Vm
(
$
#'
Vdc1 =
(
)
)
2
-,*+1
# )
)
)
:
cos α 1
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
Vdc 2 =
3 3Vm
π
' % %$ '
cos α 2 :
)
) )
"
)
)
#
Vdc1 = −Vdc 2 cos α 2 = − cos α 1 = cos(π − α 1 )
α 2 = π − α1 ( ( ) 3 ;" )$ 3 ;" ) 3 ;"
)8-
'
= =
(--
#!
(60
:
2 (.*+,% 2 4.*+,% ( ( )
: ) $3 ) ()$ 3 ;" 2 (;" 2 (.*+,% 3 ;"#. 2 (*+,%# *+,% 3 < ,;" *+.42 (*+,% 3 < ,;" 2 4*+1% )$ 3 )$ () 3 < ,;" 2 (*+.% ) 3 ) () 3 < ,;" 2 40*+1% )8. ) ) ) *+14 -52 5 *4 - : ) 3 )8-4)8. 3 ) $()$ 3 < ,;"> 2 4*+1%( 2 (*+.%A 3 < ,;"#. 2 (*+1% .*+,% 3 ,;" 2 (*+1% $ ": ωt 1 i r (t ) = v r d (ωt ) ωLr π / 6+α1 =
>?
) 2
1 ωL r
ωt
-
.
)
)
3Vm cos(ωt − π / 6)d (ωt )
π / 6+α1
3Vm [sin(ωt − π / 6]ωπ t/ 6+α1 ωL r 3Vm [sin(ωt − π / 6) − sin α1 ] ωL r )
@
""
7 #?
A
!
" #
$ # "%
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
'-
4 83
T1
T3
T5
7 )
$
)8
$
T6
T4
T2
'/
( '/ '0
'0 '1
'1 '-
)
'- '. )$
)
6
*+. )
'. ',
', '/ ) ,*+.
*
'0 '1
.*
)$
)
'/ '0
2
0*+.
) 2
6 )8 )$
) 6 6
'-
)
)$
*+1
)$
)$
)
9 *+1
0*+1
--*+1
)$ 2
-,*+1
2
'/
6
2
6
2 8
6
2
& #! ' & '
(
(6-
"$ '1 ) *+14 52 5*+.4
(
(
) )
2 3 *+14
(--
(
) )
# #
*+,# ''-
'1
-(. .(, ,(/ /(0 0(1 # ( ( ) )$
1(-# #
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
2 3 *+.4 ""
'
'.
# ) *+.4 52 50*+14 '( ( ) : ) 3 ;" 2 )$ 3 ;" 2 (.*+,% ) 3 ;" 2 4.*+,% ( ( ) : ) $3 ) ()$ 3 ;" 2 (;" 2 (.*+,% 3 ;"#. 2 (*+,%# *+,% 3 < ,;" *+.42 (*+,% 3 < ,;" 2 4*+1% )$ 3 )$ () 3 < ,;" 2 (*+.% ) 3 ) () = 3Vmsin( t+ /2) ) ) ": π / 2 +α 6 Vdc = v ab d (ωt ) 2π π / 6+α = = = = = =
'
"
Vn =
(--
3
π
π / 2 +α
" )
(6.
)
$
""
'.
# '1 ( (
)
)
#
3Vm sin(ωt + π / 6)d (ωt )
π / 6 +α
3 3Vm
[− cos(ωt + π / 6)]ππ // 26++αα
3 3Vm
[− cos(π / 2 + α + π / 6) + cos(π / 6 + α + π / 6)]
3 3Vm
[cos(π / 3 + α ) − cos(2π / 3 + α )]
π
π
π
3 3Vm
π
3 3Vm
π
.2 sin(π / 2 + α ) sin(π / 6) cos α
" =" " ) 3 3Vm Vdm =
'
'
'1
)
π
)
36
)
:
:
Vdc = cos α Vdm )
":
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
Vrms
π / 2+α
6 = 2π
1/ 2
3V sin (ωt + π / 6)d (ωt ) 2 m
2
π / 6 +α
3 3Vm2 = . π 2
1/ 2
π / 2 +α
(1 − cos(2ωt + π / 3))d (ωt )
π / 6 +α
9Vm2 sin( 2ωt + π / 3) ωt − = 2π 2 =
π / 2 +α
1/ 2
π / 6 +α
sin(π / 3 + 2α + π / 3) sin(π + 2α + π / 3) π /2 +α − −π / 6 −α + 2 2 2π
3Vm
3Vm π 1 = − {sin( 4π / 3 + 2α ) − sin(2π / 3 + 2α )} 2π 3 2 3Vm π 1 = − .2 cos(π + 2α ) sin(π / 3) 2π 3 2 3Vm π 3 cos 2α = + 2 2π 3
>?
(--
#!
= Vm = Vm
3 9 3 cos 2α + 2 4π
(6,
1/ 2
1/ 2
1/ 2
1 3 3 cos 2α + 2 4π )
1/ 2
1/ 2
9 π 9 3 . + . cos 2α 2π 3 2π 2
= 3Vm
1/ 2
1/ 2
@
""
7 #?
A
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
+. 44 T1
T3
T5
)8-
$
+. ( 4
) +. 4
) +. ( (
'/+
'1+
'.+
+
8
)8.
8
)8
$+
+
T6
T4
( '1+ '-+ '/ '0 )
'-+ '.+ '0 '1
'.+ ',+ '1 '-
6
(
*+. )
'/+ '0+ '. ',
'0+ '1+ ', '/ )
'1+ '-+ '/ '0
,*+.
*
'-+ '.+ '0 '1
.*
)$
)
'-+
4
',+ '/+ '- '. )$
)
',+
'0+
T2
2
0*+.
) 2
6 )8)$
) 6
)
)$
)$
)$
)
9 *+1
()8.
)$ 2
--*+1
2 6
)
6
*+1
0*+1
& #! ' &
(
(
) -
(
.
(--
(6/
π
" -
# )
$ B ( ($ B # )
$ .
) (
) "
)
3 3Vm
(
$
#'
Vdc1 =
(
)
)
2
-,*+1
# )
)
)
:
cos α 1
!
" #
$ # "%
Telephone : PABX : 9661920-73/4980
DEPT. OF APPLIED PHYSICS, ELETRONICS & COMMUNICATION ENGINEERING UNIVERSITY OF DHAKA DHAKA-1000, BANGLADESH FAX: 880-2-8615583 E-MAIL: [email protected]
! "
November 25, 2008 Dated, the………………………….
Ref. No............................
Vdc 2 =
3 3Vm
π
' % %$ '
cos α 2 :
)
) )
"
)
)
#
Vdc1 = −Vdc 2 cos α 2 = − cos α 1 = cos(π − α 1 )
α 2 = π − α1 ( ( ) 3 ;" )$ 3 ;" ) 3 ;"
)8-
'
= =
(--
#!
(60
:
2 (.*+,% 2 4.*+,% ( ( )
: ) $3 ) ()$ 3 ;" 2 (;" 2 (.*+,% 3 ;"#. 2 (*+,%# *+,% 3 < ,;" *+.42 (*+,% 3 < ,;" 2 4*+1% )$ 3 )$ () 3 < ,;" 2 (*+.% ) 3 ) () 3 < ,;" 2 40*+1% )8. ) ) ) *+14 -52 5 *4 - : ) 3 )8-4)8. 3 ) $()$ 3 < ,;"> 2 4*+1%( 2 (*+.%A 3 < ,;"#. 2 (*+1% .*+,% 3 ,;" 2 (*+1% $ ": ωt 1 i r (t ) = v r d (ωt ) ωLr π / 6+α1 =
>?
) 2
1 ωL r
ωt
-
.
)
)
3Vm cos(ωt − π / 6)d (ωt )
π / 6+α1
3Vm [sin(ωt − π / 6]ωπ t/ 6+α1 ωL r 3Vm [sin(ωt − π / 6) − sin α1 ] ωL r )
@
""
7 #?
A
!
" #
$ # "%
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