Single phase AC circuit.ppt

AC Circuits

2. 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

4. AC Definitions :
One effective ampereis that ac current for
which the power is the same as for one
ampere of dc current.
One effective voltis that ac voltage that
gives an effective ampere through a
resistance of one ohm.
Effective current: i
eff= 0.707 i
max
Effective voltage: V
eff= 0.707 V
max

5. Pure Resistance in AC Circuits
A
a.c. Source
R
V
Voltage and current are in phase, and Ohm’s
law applies for effective currents and voltages.
Ohm’s law: V
eff = i
effR
V
max
i
max
Voltage
Current

6. AC and Inductors :
Time, t
I
i
Current
Rise
t
0.63I
Inductor
The voltage V peaks first, causing rapid rise in i
current which then peaks as the emfgoes to zero.
Voltage leads (peaks before)the current by 90
0
.
Voltage and current are out of phase.
Time, t
I
i
Current
Decay
t
0.37I
Inductor

7. A Pure Inductor in AC Circuit
A
L
V
a.c.
V
max
i
max
Voltage
Current
The voltage peaks 90
0
before the current peaks.
One builds as the other falls and vice versa.
The reactancemay be defined as the non-resistive
oppositionto the flow of ac current.

8. Inductive Reactance
A
L
V
a.c.
The back emfinduced
by a changing current
provides opposition to
current, called inductive
reactance X
L.
Such losses are temporary, however, since the
current changes direction, periodically re-supplying
energy so that no net power is lost in one cycle.
Inductive reactance X
Lis a function of both the
inductance and the frequencyof the ac current.

9. Calculating Inductive Reactance
A
L
V
a.c.
Inductive Reactance:2 Unit is the
LX fL Ohm's law:
LLV iX
The voltagereading V in the above circuit at
the instant the accurrent is ican be found from
the inductancein Hand the frequencyin Hz.(2 )
LV i fL
Ohm’s law: V
L = i
effX
L

10. AC and Capacitance
Time, t
Q
max
q
Rise in
Charge
Capacitor
t
0.63 I
Time, t
I
i
Current
Decay
Capacitor
t
0.37 I
The voltage Vpeaks ¼ of a cycle after the
current ireaches its maximum. The voltage lags
the current. Current iand V out of phase.

11. A Pure Capacitor in AC Circuit
V
max
i
max
Voltage
CurrentA
V
a.c.
C
The voltage peaks 90
0
afterthe current peaks.
One builds as the other falls and vice versa.
The diminishing current ibuilds charge on C
which increases the back emfof V
C.

12. Capacitive Reactance
No net power is lost in a complete cycle, even
though the capacitor does provide non-resistive
opposition (reactance) to the flow of ac current.
Capacitive reactance X
Cis affected by both the
capacitanceand the frequency of the ac current.
A
V
a.c.
CEnergygains and losses
are also temporary for
capacitors due to the
constantly changing ac
current.

13. Calculating capacitive Reactance
Capacitive Reactance:1
Unit is the
2
CX
fC
 Ohm's law: V
CCiX
The voltagereading V in the above circuit at
the instant the accurrent is ican be found from
the inductancein Fand the frequencyinHz.2
L
i
V
fL

A
V
a.c.
C
Ohm’s law: V
C = i
effX
C

14. Frequencyand AC Circuits
f
R, X1
2
CX
fC
 2
LX fL
ResistanceRis constant and not affected by f.
Inductive reactance X
L
varies directly with
frequency as expected
since EDi/Dt.
Capacitive reactance X
Cvaries
inverselywithfsince rapid ac
allows little time for charge to
build up on capacitors.
R
X
LX
C

15. Series LRC Circuits
L
V
R V
C
CR
a.c.
V
L
V
T
A
Series ac circuit
Consider an inductor L, a capacitor C, and
a resistor Rall connected in serieswith an
ac source. The instantaneous current and
voltages can be measured with meters.

16. Phasein a Series AC Circuit
The voltage leadscurrent in an inductor and lags
current in a capacitor. In phasefor resistance R.
q
45
0
90
0
135
0
180
0
270
0
360
0
V
V= V
max sin q
V
R
V
C
V
L
Rotating phasordiagram generates voltage waves
for each element R, L, and C showing phase
relations. Current iis alwaysin phase with V
R.

17. Phasorsand Voltage
At time t = 0, suppose we read V
L, V
Rand V
Cfor an
ac series circuit. What is the source voltage V
T?
We handle phase differences by finding the
vector sum of these readings. V
T= S V
i. The
angle qis the phase angle for the ac circuit.
q
V
R
V
L -V
C
V
T
Source voltage
V
R
V
C
V
L
Phasor
Diagram

18. Calculating Total Source Voltage
q
V
R
V
L -V
C
V
T
Source voltageTreating as vectors, we find:22
()
T R L C
V V V V   tan
LC
R
VV
V



Now recall that:V
R= iR; V
L= iX
L;andV
C= iV
C
Substitution into the above voltage equation gives:22
()
T L C
V i R X X  

19. Impedance in an AC Circuit

R
X
L -X
C
Z
Impedance22
()
T L C
V i R X X  
Impedance Z is defined:22
()
LC
Z R X X  
Ohm’s law for ac current
and impedance: or
T
T
V
V iZ i
Z

The impedanceis the combined opposition to ac
current consisting of both resistance and reactance.

20. Resonant Frequency
Becauseinductancecauses the voltage to lead
the current and capacitancecauses it to lagthe
current, they tend to canceleach other out.
Resonance(Maximum Power)
occurs when X
L = X
C
R
X
C
X
LX
L= X
C22
()
LC
Z R X X R    1
2
2
fL
fC


 1
2
r
f
LC

Resonantf
r
X
L= X
C

21. Power in an AC Circuit
No power is consumed by inductance or
capacitance. Thus power is a function of the
component of the impedance along resistance:
In terms of ac voltage:
P = iV cos 
In terms of the resistance R:
P = i
2
R

R
X
L -X
C
Z
Impedance
P lost in Ronly
The fraction Cos is known as the power factor.

22. Summary
Effective current: i
eff= 0.707 i
max
Effective voltage: V
eff= 0.707 V
max
Inductive Reactance:2 Unit is the
LX fL Ohm's law:
LLV iX Capacitive Reactance:1
Unit is the
2
CX
fC
 Ohm's law: V
CCiX

23. Summary (Cont.)22
()
T R L C
V V V V   tan
LC
R
VV
V


 22
()
LC
Z R X X   or
T
T
V
V iZ i
Z
 tan
LCXX
R


 1
2
r
f
LC


24. Summary (Cont.)
In terms of ac voltage:
P = iV cos 
In terms of the resistance R:
P = i
2
R
Power in AC Circuits: