L20 1 ph-ac
9
ELE101/102 Dept of E&E,MIT Manipal 1 Series RL Circuit ) ( ) ( ; V ; ; 90 90 V form polar in quantities the all represent us let and axis reference the be I Let 0 I I t; sin ) ( let L t sim V t v V IR V V LI j IX I t i m R L L m R L v(t) i(t) Phasor Diagram - V I X LI V L L 90º I Referenc e (phasor) IR V R
description
Transcript of L20 1 ph-ac
ELE101/102 Dept of E&E,MIT Manipal 1
Series RL Circuit
)()(
; V
;;90 90V
formpolar in quantities
theall represent uslet and axis reference thebe ILet
0II t;sin)(let
L
tsimVtv
V
IRVVLIjIX
Iti
m
RLL
m
R L
v(t) i(t)
Phasor Diagram -
V IXLIV LL
90ºI
Reference (phasor)
IRVR
ELE101/102 Dept of E&E,MIT Manipal 2
Series RL Circuit - Complex Impedance
R
LXRZ
ZXZR
jZ
ZZjXRZ
ZIIjXR
IjXIRVVV
L
L
L
L
LLR
122 tan;)(or
sin;cos
)sin(cos
)(ˆ
ˆ)(
IZV IXLIV LL
90ºI
Reference (phasor)
IRVR
Z LXL
90ºI
Reference (phasor)
R
The phase difference between V & I is termed as phase angle , .
Cosine of the angle is called Power factor (Pf)
ELE101/102 Dept of E&E,MIT Manipal 3
Series RL Circuit….
)t(simV)t(v
ωtsinI)t(i
m
m
t/2 3/2 2
v
i
The current lags behind the voltage by a phase angle
ELE101/102 Dept of E&E,MIT Manipal 4
Series RL Circuit – Power consumed
Instantaneous power)t(i)t(v)t(p
2coscos
2coscos2
tVI
tIV mm
tsinItsinV mm
Average power
2
0
)()(2
1wtdtpP cos
2
IV mm
cosVIP Cos is called the power factor
ELE101/102 Dept of E&E,MIT Manipal 5
Series RC Circuit – Phasor diagram
)sin()(
; V
;
90V
formpolar in quantities
theallrepresent uslet and axis reference thebe ILet
0sin
C
tVtv
V
IRVIjXCj
I
IX
Iωt ILet i(t)
m
RC
C
m
Phasor Diagram -
V IXV CC
-90º IReference
(phasor)IRVR
R C
v(t) i(t)
ELE101/102 Dept of E&E,MIT Manipal 6
Series RC Circuit - Complex Impedance
CR
1tan;)XRZ
sinZX;cosZR
)sinj(cosZ
ZZ)jXRZ
ZII)jXR
IjXIRVVV
12C
2
C
C
C
CCR
(or
(
( IZV IXV CC
-90º IReference
(phasor)IRVR
ZC
1X C
-90º IReference
(phasor)R
ELE101/102 Dept of E&E,MIT Manipal 7
Series RC Circuit….
)t(simV)t(v
ωtsinI)t(i
m
m
The current Leads behind the voltage by a phase angle
t/2 3/2 2
v
i
ELE101/102 Dept of E&E,MIT Manipal 8
Series RC Circuit – Power consumed
Instantaneous power)t(i)t(v)t(p
tVI
tIV mm
2coscos
2coscos2
tsinItsinV mm
Average power
2
0
)()(2
1wtdtpP cos
2
IV mm
cosVIPCos is called the power factor
ELE101/102 Dept of E&E,MIT Manipal 9
Series RLC Circuit
Let i(t) = Im sint
Impedance, Z=R+j(XL-XC)
(i) If XL=XC , resistive circuit
(ii) If XL>XC, RL series circuit
(iii) If XL<XC, RC series circuit
L
v(t) i(t)
R C
Note: - i(t) is the reference
