Embed Size (px)
Citation preview
Roll No. Name
41. RATIYA RAJU
42. SATANI DARSHANA
43. SAVALIYA MILAN
44. SISARA GOVIND
45. VALGAMA HARDIK
46. VADHER DARSHAK
47. VADOLIYA MILAN
48. VALA GOPAL
49. SHINGADIYA SHYAM
50. KARUD LUKMAN
AC Definitions :
One One effective ampereeffective ampere is that ac is that ac current for which the power is the current for which the power is the same as for one ampere of dc current.same as for one ampere of dc current.
One One effective volteffective volt is that ac voltage is that ac voltage that gives an effective ampere that gives an effective ampere through a resistance of one ohm.through a resistance of one ohm.
Effective current: ieff = 0.707 imax
Effective current: ieff = 0.707 imax
Effective voltage: Veff = 0.707 Vmax
Effective voltage: Veff = 0.707 Vmax
Pure Resistance in AC Circuits
A
a.c. Source
R
V
Voltage and current are in phase, and Voltage and current are in phase, and Ohm’s law applies for effective currents Ohm’s law applies for effective currents
and voltages.and voltages.
Voltage and current are in phase, and Voltage and current are in phase, and Ohm’s law applies for effective currents Ohm’s law applies for effective currents
and voltages.and voltages.
Ohm’s law: Veff = ieffR
Vmax
iimaxmax
Voltage
Current
AC and Inductors :
Time, t
I i
Current Current RiseRise
0.63I
Inductor
The voltage The voltage V V peaks first, causing rapid rise peaks first, causing rapid rise in in i i current which then peaks as the emf current which then peaks as the emf goes to zero. Voltage goes to zero. Voltage leads (peaks before)leads (peaks before) the current by 90the current by 9000. . Voltage and current are Voltage and current are out of phaseout of phase..
Time, t
I i
Current Current DecayDecay
0.37I
Inductor
A Pure Inductor in AC Circuit
A
L
V
a.c.
Vmax
iimaxmax
Voltage
Current
The voltage peaks 90The voltage peaks 900 0 before the current before the current peaks. One builds as the other falls and peaks. One builds as the other falls and
vice versa.vice versa.
The voltage peaks 90The voltage peaks 900 0 before the current before the current peaks. One builds as the other falls and peaks. One builds as the other falls and
vice versa.vice versa.The The reactancereactance may be defined as the may be defined as the non-non-resistiveresistive oppositionopposition to the flow of ac current. to the flow of ac current.
Inductive Reactance
A
L
V
a.c.
The The back emf back emf induced by a induced by a changing current changing current provides opposition provides opposition to current, called to current, called inductiveinductive reactance reactance XXLL..Such losses are Such losses are temporarytemporary, however, since , however, since the current the current changes directionchanges direction, periodically , periodically re-supplying energy so that no net power is re-supplying energy so that no net power is lost in one cycle.lost in one cycle.Inductive reactance XInductive reactance XLL is a function of is a function of both the both the inductance inductance and the and the frequencyfrequency of of the ac current.the ac current.
Calculating Inductive Reactance
A
L
V
a.c.
Inductive Reactance:2 Unit is the LX fL
Ohm's law: L LV iX
The The voltagevoltage reading reading V V in the above circuit in the above circuit at the instant the at the instant the acac current is current is ii can be can be found from the found from the inductanceinductance in in HH and the and the frequencyfrequency in in HzHz..
(2 )LV i fL (2 )LV i fL Ohm’s law: VL = ieffXL
AC and Capacitance
Time, t
Qmaxq
Rise in Rise in ChargeCharge
Capacitor
0.63 I
Time, t
I i
Current Current DecayDecay
Capacitor
0.37 I
The voltage The voltage VV peaks ¼ of a cycle after the peaks ¼ of a cycle after the current current ii reaches its maximum. The voltage reaches its maximum. The voltage lagslags the current. the current. Current Current ii and V out of and V out of phasephase..
A Pure Capacitor in AC Circuit
Vmax
iimaxmax
Voltage
CurrentA V
a.c.
C
The voltage peaks 90The voltage peaks 900 0 afterafter the current the current peaks. One builds as the other falls and peaks. One builds as the other falls and
vice versa.vice versa.
The voltage peaks 90The voltage peaks 900 0 afterafter the current the current peaks. One builds as the other falls and peaks. One builds as the other falls and
vice versa.vice versa.The diminishing current The diminishing current ii builds charge on builds charge on
C C which increases the which increases the back emf back emf of of VVC.C.
The diminishing current The diminishing current ii builds charge on builds charge on C C which increases the which increases the back emf back emf of of VVC.C.
Capacitive Reactance
No No net power net power is lost in a complete cycle, is lost in a complete cycle, even though the capacitor does provide non-even though the capacitor does provide non-resistive opposition (resistive opposition (reactancereactance) to the flow of ) to the flow of ac current.ac current.Capacitive reactance XCapacitive reactance XCC is affected by both is affected by both the the capacitancecapacitance and the and the frequency frequency of the of the ac current.ac current.
A V
a.c.
CEnergyEnergy gains and gains and losses are also losses are also temporary temporary for for capacitors due to the capacitors due to the constantly changing constantly changing ac current.ac current.
Calculating capacitive Reactance
Capacitive Reactance:1
Unit is the 2CX fC
Ohm's law: VC CiX
The The voltagevoltage reading reading V V in the above circuit in the above circuit at the instant the at the instant the acac current is current is ii can be can be found from the found from the inductanceinductance in in FF and the and the frequencyfrequency in in Hz Hz..
2L
iV
fL
2L
iV
fL
A V
a.c.
C
Ohm’s law: VC = ieffXC
Frequency and AC Circuits
ff
R, XR, X
1
2CX fC
1
2CX fC2LX fL
ResistanceResistance R R is constant and not affected is constant and not affected by by f.f.
Inductive reactance XInductive reactance XL L
varies directly with varies directly with frequency as expected frequency as expected since since EE i/i/tt..
Capacitive reactance Capacitive reactance XXCC
variesvaries inverselyinversely with with ff since rapid ac allows little since rapid ac allows little time for charge to build up time for charge to build up on capacitors.on capacitors.
RR
XXLLXXCC
Series LRC Circuits
L
VR VC
CRa.c.
VL
VT
A
Series ac circuit
Consider an Consider an inductor inductor LL, , a a capacitor capacitor CC, , and a and a resistor resistor RR all connected in all connected in seriesseries with with an ac sourcean ac source. The . The instantaneous current and voltages instantaneous current and voltages can be measured with meters.can be measured with meters.
Consider an Consider an inductor inductor LL, , a a capacitor capacitor CC, , and a and a resistor resistor RR all connected in all connected in seriesseries with with an ac sourcean ac source. The . The instantaneous current and voltages instantaneous current and voltages can be measured with meters.can be measured with meters.
Phase in a Series AC CircuitThe voltage The voltage leadsleads current in an inductor current in an inductor and and lagslags current in a capacitor. current in a capacitor. In phaseIn phase for for
resistance resistance RR..
450 900 1350
1800 2700 3600
V V = Vmax sin
VRVC
VL
Rotating Rotating phasor diagram phasor diagram generates voltage generates voltage waves for each element waves for each element RR, , LL, and , and C C showing showing phase relations. Current phase relations. Current i i is always is always in in phase phase with with VVR.R.
Phasors and VoltageAt time t = 0, suppose we read At time t = 0, suppose we read VVLL, , VVRR and and VVCC
for an ac series circuit. What is the source for an ac series circuit. What is the source voltage voltage VVTT??
We handle phase differences by finding We handle phase differences by finding the the vector sum vector sum of these readings. of these readings. VVTT = = VVii. . The angle The angle is the is the phase angle phase angle for for the ac circuit.the ac circuit.
VR
VL - VCVVTT
Source voltageSource voltage
VRVC
VL
Phasor Phasor DiagraDiagra
mm
Calculating Total Source Voltage
VR
VL - VCVVTT
Source voltageSource voltage Treating as vectors, we Treating as vectors, we find:find:
2 2( )T R L CV V V V 2 2( )T R L CV V V V
tan L C
R
V V
V
tan L C
R
V V
V
Now recall that:Now recall that: VVRR = iR = iR; ; VVLL = iX = iXLL;; andand VVCC = iV = iVCC
Substitution into the above voltage equation Substitution into the above voltage equation gives:gives:
2 2( )T L CV i R X X 2 2( )T L CV i R X X
Impedance in an AC Circuit
R
XL - XCZZ
ImpedanceImpedance2 2( )T L CV i R X X
2 2( )T L CV i R X X
Impedance Impedance Z Z is is defined:defined:
2 2( )L CZ R X X 2 2( )L CZ R X X
Ohm’s law for ac Ohm’s law for ac current and current and impedance:impedance:
or TT
VV iZ i
Z or T
T
VV iZ i
Z
The impedance is the combined opposition to ac current consisting of both resistance and reactance.
The impedance is the combined opposition to ac current consisting of both resistance and reactance.
Resonant Frequency
BecauseBecause inductanceinductance causes the voltage to causes the voltage to leadlead the current and the current and capacitancecapacitance causes it causes it to to laglag the current, they tend to the current, they tend to cancelcancel each each other out.other out.
BecauseBecause inductanceinductance causes the voltage to causes the voltage to leadlead the current and the current and capacitancecapacitance causes it causes it to to laglag the current, they tend to the current, they tend to cancelcancel each each other out.other out.
ResonanceResonance (Maximum (Maximum Power) occurs when XPower) occurs when XL L = =
XXCCRXC
XL XXLL = = XXCC
2 2( )L CZ R X X R 2 2( )L CZ R X X R
12
2fL
fC
1
2rf
LC
1
2rf
LCResonantResonant
ffrr X XLL = X = XC C
Power in an AC Circuit
No power is consumed by inductance or No power is consumed by inductance or capacitance. Thus power is a function of capacitance. Thus power is a function of the component of the impedance along the component of the impedance along
resistance:resistance:
No power is consumed by inductance or No power is consumed by inductance or capacitance. Thus power is a function of capacitance. Thus power is a function of the component of the impedance along the component of the impedance along
resistance:resistance:In terms of ac In terms of ac
voltage:voltage:P = iV cos P = iV cos
In terms of the resistance In terms of the resistance R:R:
P = i2RP = i2R
R
XL - XCZZ
ImpedanceImpedance
P P lost in lost in RR only only
The fraction The fraction Cos Cos is known as the is known as the power power factor. factor.
Summary
Effective current: ieff = 0.707 imax
Effective current: ieff = 0.707 imax
Effective voltage: Veff = 0.707 Vmax
Effective voltage: Veff = 0.707 Vmax
Inductive Reactance:2 Unit is the LX fL
Ohm's law: L LV iX
Capacitive Reactance:1
Unit is the 2CX fC
Ohm's law: VC CiX
Summary (Cont.)
2 2( )T R L CV V V V 2 2( )T R L CV V V V tan L C
R
V V
V
tan L C
R
V V
V
2 2( )L CZ R X X 2 2( )L CZ R X X
or TT
VV iZ i
Z or T
T
VV iZ i
Z
tan L CX X
R
tan L CX X
R
1
2rf
LC
1
2rf
LC
Summary (Cont.)
In terms of ac In terms of ac voltage:voltage:
P = iV cos P = iV cos
In terms of the resistance In terms of the resistance R:R:
P = i2RP = i2R
Power in AC CircuitsPower in AC Circuits::
