basic ac circuits
TRANSCRIPT
Chapter 4R-L-C A.C. CIRCUIT
SERIES RESONANCEA.C. POWER TRIANGLE
POWER FACTOR CORRECTION
R-L-C AC CIRCUIT
Pure Resistive AC Circuit
Pure Capacitive AC Circuit
Pure Inductive AC Circuit
Circuit
PhasorDiagram
I-VWaveform
current IR and applied voltage VR are in phase
current IL lagging theapplied voltage VL by 90◦
current IC leading the applied voltage VC by 90◦
Reactance R
in a capacitor (C) the current (I) leads voltage (V), and voltage (V) leads
current (I) in an inductor (L).
C-I-V-I-L
Impedance, Z = Opposition for current to change (or to flow) in circuit due to capacitance (capacitive reactance, XC) AND inductance (inductive reactance, XL) (unit=ohm, Ω)
Reactance, X = Opposition to a change in current (or to flow) due to capacitance (capacitive reactance, XC) OR inductance (inductive reactance, XL)
Terms
Example1 2
Exercise1
3
2
12
3
45
6
TUTORIAL
RC Series Circuit
Phasor Diagram
Example1 2
Exercise1
3
2
4
5
89
10
11
TUTORIAL
1234
567
R-L-C Series Circuit
Z
@
Capacitive CircuitInductive Circuit
Resonance
Example1
Example
Exercise1
2
TUTORIAL
1
2
3
SERIES RESONANCE
Properties
Phasor Diagram
Resonance
Properties
7 Things you need to know about RLC Series Circuits.
1. AT RESONANCE (ƒr) XC is equal to XL (but in anti-phase)2. AT RESONANCE (ƒr) VC is equal to VL (but in anti-phase)3. AT RESONANCE (ƒr) Impedance (Z) is at minimum and equal to the
RESISTANCE (R)4. AT RESONANCE (ƒr) Circuit current is at a maximum.5. AT RESONANCE (ƒr) The circuit is entirely resistive.6. BELOW RESONANCE (ƒr) The circuit is capacitive.7. ABOVE RESONANCE (ƒr) The circuit is inductive.
Q-FactorResonance
Example1 2
Example Exercise1
2
3
TUTORIAL
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6
BandwidthResonance
Bandwidth
Example
POWER TRIANGLE
D.C. POWER TRIANGLE
A.C. POWER TRIANGLE
(a) For a purely resistive a.c. circuit, the average power dissipated, P, is given by: P=VI=I2R= V2/R watts (V and I being r.m.s. values) See Fig.(a)
(b) For a purely inductive a.c. circuit, the average power is zero. See Fig.(b)
(c) For a purely capacitive a.c. circuit, the average power is zero. See Fig.(c)
A.C. POWER TRIANGLE
Example1
Exercise1
𝑉 𝑟𝑚𝑠=𝑉𝑀𝑎𝑥
√2
𝐼 𝑟𝑚𝑠=𝐼𝑀𝑎𝑥
√2
𝑉=𝑉𝑚𝑎𝑥𝑆𝑖𝑛𝜔𝑡𝐼=𝐼𝑚𝑎𝑥𝑆𝑖𝑛𝜔𝑡
Power Triangle
Apparent power (VA)
Real power (Watt)
Reactive power (VAR)
Power Triangle Analogy
Apparent power (VA)
Real power (Watt)
Reactive power (VAR)
Example1
Exercise1
2
2
3
1
23
4
56
TUTORIAL 78
9
10
POWER FACTOR CORRECTION
Low Power Factor
High Power Factor
REAL
‘TEH
’RE
AL P
OW
ER
REAL
‘TEH
’RE
AL P
OW
ER
‘WASTED” Reactive‘WASTED” Reactive
Power Factor Correction
• In any a.c. circuit, power factor = cos θ, where θ is the phase angle between supply current and supply voltage.
Power Factor Correction
• Industrial loads such as a.c. motors are essentially inductive (i.e. R-L) and may have a low power factor.
• For example, let a motor take a current of 50A at a power factor of 0.6 lagging from a 240V, 50Hz supply, as shown below.
?
How can this power factor of 0.6 be ‘improved’ or ‘corrected’ to, say, unity?
Power Factor Correction• Unity power factor means: cos θ = 1
from which, θ = 0• How can the circuit being modified and that circuit phase
angle is changed from 53.13◦ to 0◦?• The answer is to connect a capacitor in parallel with the
motor as shown belowWhen a capacitor is connected in parallel with the inductive load, it takes a current shown as IC . In the phasor diagram, the current IC is shown leading the voltage V by 90◦
The supply current is shown as I and is now the phasor sum of IM and IC.
Power Factor Correction
• In the phasor diagram, current I is shown as the phasor sum of IM and IC and is in phase with V , i.e. the circuit phase angle is 0◦, which means that the power factor is cos 0◦ = 1.
• Thus, by connecting a capacitor in parallel with the motor, the power factor has been improved from 0.6 lagging to unity.
53.13O
IM
IS
ISa
b
Power Factor Correction• Before the capacitor was connected, the supply current was
50A. Now it is 30A.• In conclusion, the advantage of power factor improvement –
the supply current has been reduced.• When power factor is improved, the supply current is
reduced, the supply system has lower losses (i.e. lower I2R losses) and therefore cheaper running costs.
Example1
Power Factor Correction
• In practical situations a power factor of 1 is not normally required but a power factor in the region of 0.8 or better is usually aimed for. (Actually, a power factor of 1 means resonance!)
Example2
Exercise
2
1 1TUTORIAL
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5TUTORIAL
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46
Thank You