vsvs l c r at every instant, the generator / supply voltage: (v s = v m sinωt) is given by: v s = v...
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![Page 1: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/1.jpg)
VS
L C R
At every instant, the generator / supply voltage: (VS = Vmsinωt) is given by:
VS = VL + VC + VR
IZ = IXL + IXC + IR
These relationships can best be shown on a PHASOR DIAGRAM
LCR Circuit
![Page 2: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/2.jpg)
R C L
RV CV LV
V
RV
I
CV
LV
V
VL
VR
VC
I
ω
PhasorDiagram
![Page 3: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/3.jpg)
See 6 RLC circuits applet
![Page 4: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/4.jpg)
LCR Circuit ~ Phasor Diagram VL
VR
VC
I
ω
VR and I are IN PHASE
VL Leads I by 90o
VC LAGS I by 90o
fL
fC
2XIXV
2
1XIXV
constantisRIRV
LLL
CCC
R
Total reactance (XT) in the circuit is the difference between XL and XC
(XL – XC or XC – XL)
22S IZV CL XXRZ
XL- XC
XL
R
XC
R
Z
![Page 5: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/5.jpg)
IZV
XXRIV
VVVV
S
CLS
CLRS
22
22
)(
)(VL
VR
VC
Vs
Ф
IR
XX
V
VV CL
R
CL
tan
XT = XL- XC ie XL > XC
XT = XC- XL ie XC > XL
Phase angle between Voltage supply and Current (or VR)
![Page 6: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/6.jpg)
1. Calculate the reactance of the capacitor
2. Calculate the reactance of the inductor
3. Determine the impedance of the circuit
RCL Circuits
This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz
15 mH250 µF
5.0 Ω 50 Hz
![Page 7: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/7.jpg)
1. Calculate the reactance of the capacitor
RCL Circuits
This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz
2. Calculate the reactance of the inductor
15 mH250 µF
5.0 Ω 50 Hz
correct sig.figcorrect unit
![Page 8: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/8.jpg)
XL = 4.7 Ω
XC = 13 Ω
8.3
Ω
5.0 Ω
9.7 Ω
R = 5.0 Ω
OR
OR
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1. Determine the supply voltage Vs(rms)
2. Determine the phase difference between the current and the supply voltage
RCL Circuits
This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor.
The AC supply has a frequency of 50 Hz that provides a current IRMS = 1.2 A
The reactance of the capacitor is 13 Ω, the inductor 4.7 Ω and the impedance of the circuit is 9.7 Ω
15 mH250 µF
5.0 Ω 50 Hz
![Page 10: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/10.jpg)
1. Determine the supply voltage Vs(rms)
RCL Circuits This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor.
The AC supply has a frequency of 50 Hz that provides a current IRMS = 1.2 A
The reactance of the capacitor is
13 Ω, the inductor 4.7 Ω and the
impedance of the circuit is 9.7 Ω
2. Determine the phase difference between the current and the supply voltage
15 mH250 µF
50 Hz
VR = 5 W
VC = 13 WVL = 4.7 W
VX= 8.3 x 1.2
VR = 5.0 x 1.2
12 V
θ
By measurement
VS lagging current
by 60º ± 2º
OR
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R C L
Example
VS = 110 V f = 60 Hz
50 W 8 mF 0.8 H
a) What is the impedance of the circuit?
Z
VI
2CL2 XXRZ
22
fC21
fL2RZ
2
62
F10x8Hz602
1H8.0Hz60250Z
58
58V 110
A 9.1
b) What is the current in the circuit?
c) What is the phase angle between Vs and I ?
R
XXtan CL
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![Page 13: VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships](https://reader034.vdocuments.net/reader034/viewer/2022051417/5697bfd61a28abf838cadd3a/html5/thumbnails/13.jpg)
Tweeter
Woofer
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