Add Abstract, Introduction and Conclusion to the Inductors in DC Circuits Lab. Input calculation
Electric Circuits Lab
Instructor: ———–
Capacitors in DC Circuits
Student Name(s):
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Honor Pledge:
I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community, it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to the Judicial Review Board hearing if summoned.
Date: 1/1/2018
Contents
Abstract 3
Introduction 3
Procedures 3
Data Presentation & Analysis 4
Calculations 4
Required Screenshots 4
Conclusion 4
References 5
(This instruction box is to be deleted before submission of the Lab report)
What is an Abstract?
This should include a brief description of all parts of the lab. The abstract should be complete in itself. It should summarize the entire lab; what you did, why you did it, the results, and your conclusion. Think of it as a summary to include all work done. It needs to be succinct yet detailed enough for a person to know what this report deals with in its entirety.
Objectives of Week 3 Lab 1:
· Measure the resistance and capacitance.
· Familiarize with Oscilloscope and Function generator.
· Measure the RC time constant using VR and VC.
· Understand the effect of series and parallel capacitors on RC time constant.
Introduction
(This instruction box is to be deleted before submission of the Lab report)
What is an Introduction?
In your own words, explain the reason for performing the experiment and give a concise summary of the theory involved, including any mathematical detail relevant to later discussion in the report. State the objectives of the lab as well as the overall background of the relevant topic.
Address the following items in your Introduction:
· What is the time constant for an RC circuit and what is its significance?
· How do capacitors combine in series? (Give formula)
· How do capacitors combine in parallel? (Give formula)
· What is capacitive reactance? (Give formula)
Part I:
1.
Construct the circuit shown in
Figure 1 in Mutism.
Figure 1: Series RC Circuit
2.
Connect Channel A of the oscilloscope across the voltage source and Channel B across the capacitor.
3.
Set the function generator to
5Vpp; 100 Hz, Square Wave 50% duty cycle with 2.5 DC offset if using a function generator
. If using clock voltage, set it to 5Vpp, 100 Hz. The DC offset can be modeled by using DC mode on the oscilloscope.
4.
Observe the signals on the scope screen. See
Figure 2(a) below. (Use Volts/Div and Time/DIV settings to adjust the signal)
Figure 2(a): Voltage across the Voltage Source and the capacitor
5.
Disable Channel A, by setting it to 0, while observing Channel B. You should be able to see the waveform as shown below. Use time base and Channel A scale to adjust the signal.
Figure 2(b): Voltage across the capacitor
6
. Change the time base (Sec/Div) until you have a clear waveform on the scope as shown in
Figure 2(c).
Figure 2(c): Voltage across the capacitor
7.
Calculate the time constant of the RC circuit using the circuit parameter values.
Record the result in
Table 1 under calculated value.
= R*C
8.
Measuring the time constant with VC:
i.
Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ____5V_____.
ii.
Calculate the 63% of the above value __3.15V_______.
iii. Place the second cursor (T2) at the step (ii) value above and T1 at zero just before the capacitor voltage starts rising as shown in
Figure 3.
iv.
Observe the value of T2T1 on the scope, which is the one time constant, as shown below.
v.
Record the result in
Table 1 above under measured value using VC.
Figure 5: Measuring RC time constant using VC
9.
Connect Channel B of the oscilloscope across the resistor.
10. You should be able to see the waveform as shown below. (Use Volts/Div and Time/DIV knobs to adjust the signal)
Figure 6(a): Voltage across the resistor
11.
Measuring the time constant with VR:
·
Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ____5V_____.
·
Calculate the 37% of the above value ____1.85V_____.
· Place the second cursor (T2) at the step (ii) value above.
· Observe the T2T1 value on the scope, which is the one time constant.
·
Record the result in
Table 1 above under measured value using VR.
Figure 6(b): Measuring RC timeconstant using VR
Part II:
12.
Place two capacitors in series as shown in
Figure 7 below.
Figure 7: Series Capacitors
13.
Calculate the total capacitance value and
record the results in
Table 2.
14.
Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.
·
Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter) as shown in
Figure 8.
·
Measure the capacitive reactance, XC, as shown in
Figure 8.
·
Calculate the capacitance using the equation, and
record the value in
Table 2.
Figure 8: Impedance Meter in Multisim
15.
Modify the circuit as shown below, by placing two 0.22µF capacitors in series as in
Figure 8.
Figure 8: RC circuit with two series capacitors
16.
Calculate the new RC time constant using measured values.
Record the result in
Table 3.
17.
Connect Channel A of the oscilloscope across the resistor
18. Adjust the trigger if needed, and you should be able to see the waveform as shown in
Figure 9 below.
Figure 9: Voltage Across the Resistor
19.
Repeat step 11.
Record the measured time constant in
Table 3.
Part III:
20.
Place two capacitors in parallel as shown in
Figure 10 below. (
Note: The 0.001 Ω resistor is
ONLY required for simulation in Multisim. Without the resistor, the mathematical model will not converge).
Figure 10: Parallel Capacitors
21.
Calculate the total capacitance value and
record the results in
Table 4 below.
22.
Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.
·
Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter).
·
Measure the capacitive reactance.
·
Calculate the capacitance using the equation, and
record the value in
Table 4.
23.
Modify the circuit by placing two 0.22µF capacitors in parallel as in
Figure 11.
Figure 11: RC Circuit with Parallel Capacitors
24.
Calculate the new RC time constant using measured values.
Record the result in
Table 5.
25.
Connect Channel A of the oscilloscope across the resistor.
26. You should be able to see the waveform as in
Figure 12 below. (Use Volts/Div and Time/DIV knobs to adjust the signal)
27. Use the cursors on the oscilloscope to
measure the time constant (refer to step 11).
Record the result in
Table 5 under measured value.
Figure 12: Voltage across the resistor
Data Presentation & Analysis
Calculated value
Measured value using VC
Measured value using VR
Time constant ()
220.049us
220.015us
Table 1: Calculated and measured time constant values
Calculated Value
Measured Value
Capacitance
11µF
10.2µF
Table 2: Series Capacitors
Calculated value
Measured value using VR
Time constant ()
114.643us
Table 3: Calculated and measured time constant values
Calculated value
Measured value
Capacitance
0.44µF
0.442µF
Table 4: Parallel Capacitors
Calculated value
Measured value using VR
Time constant ()
Table 5: Calculated and measured time constant values
Calculations
(This instruction box is to be deleted before submission of the Lab report)
Show all of your calculations in this section.
Part 1 step 7: =
Part 2 step 13: CT =
Part 2 step 14: CT =
Part 2 step 16: =
Part 2 step 19: =
Part 3 step 21: CT =
Part 3 step 22: CT =
Part 3 step 24: =
(This instruction box is to be deleted before submission of the Lab report)
Place screenshots of measurements in this section. You may change the names of the figures as the ones provided show the required content.
Figure 13: Screenshot of Waveforms Part 1 Step 8
Figure 14: Screenshot of Waveforms Part 1 Step 11
Figure 15: Screenshot of Impedance Meter Part 2 Step 14
Figure 16: Screenshot of Waveforms Part 2 Step 19
Figure 17: Screenshot of Impedance Meter Part 3 Step 22
Figure 18: Screenshot of Waveforms Part 3 Step 27
(This instruction box is to be deleted before submission of the Lab report)
What is a Conclusion?
This section should reflect your understanding of the experiment conducted. Important points to include are a brief discussion of your results, and an interpretation of the actual experimental results as they apply to the objectives of the experiment set out in the introduction should be given. Also, discuss any problems encountered and how they were resolved.
Address the following in your conclusions:
· Did your measured results match your calculated values? If not, why not?
· What happened to the overall capacitance when you went from one series capacitor to two? (Did capacitance increase or decrease?)
· What happened to the overall capacitive reactance when you went from one series capacitor to two? (Did the capacitive reactance increase or decrease?)
· What happened to the time constant when you went from one series capacitor to two? (Did the time constant increase or decrease?)
· What happened to the overall capacitance when you went from one capacitor to two parallel capacitors? (Did the capacitance increase or decrease?)
· What happened to the overall capacitive reactance when you went from one capacitor to two parallel capacitors? (Did the capacitive reactance increase or decrease?)
· What happened to the time constant when you went from one capacitor to two parallel capacitors? (Did the time constant increase or decrease?)
Floyd, T. L., & Buchla, D. M. (2019).
Principles of Electric Circuits (10th Edition). Pearson Education (US).
https://bookshelf.vitalsource.com/books/9780134880068
(2017) National Instruments Multisim (V 14.1) [Windows]. Retrieved from http://www.ni.com/multisim/
6
Electric Circuits Lab
Capacitors in DC Circuits
I.
Objectives:
After completing this lab experiment, you should be able to:
· Measure the resistance and capacitance.
· Familiarize with Oscilloscope and Function generator.
· Measure the RC time constant using VR and VC.
· Understand the effect of series and parallel capacitors on RC time constant.
II.
Parts List:
· Resistor (1) 1 kΩ
· Capacitors (2) 0.22 µF
III.
Procedures:
Part I:
1.
Construct the circuit shown in
Figure 1 in Mutism.
Figure 1: Series RC Circuit
2.
Connect Channel A of the oscilloscope across the voltage source and Channel B across the capacitor.
3.
Set the function generator to
5Vpp; 100 Hz, Square Wave 50% duty cycle with 2.5 DC offset if using a function generator
. If using clock voltage, set it to 5Vpp, 100 Hz. The DC offset can be modeled by using DC mode on the oscilloscope.
4.
Observe the signals on the scope screen. See
Figure 2(a) below. (Use Volts/Div and Time/DIV settings to adjust the signal)
Figure 2(a): Voltage across the Voltage Source and the capacitor
5.
Disable Channel A, by setting it to 0, while observing Channel B. You should be able to see the waveform as shown below. Use time base and Channel A scale to adjust the signal.
Figure 2(b): Voltage across the capacitor
6. Change the time base (Sec/Div) until you have a clear waveform on the scope as shown in
Figure 2(c).
Figure 2(c): Voltage across the capacitor
7.
Calculate the time constant of the RC circuit using the circuit parameter values.
Record the result in
Table 1 under calculated value.
= R*C
Calculated value 
Measured value using VC 
Measured value using VR 

Time constant () 
220.049us 
220.015us 
Table 1: Calculated and measured values
8.
Measuring the time constant with VC:
i.
Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ___5V______.
ii.
Calculate the 63% of the above value _____3.15 V____.
iii. Place the second cursor (T2) at the step (ii) value above and T1 at zero just before the capacitor voltage starts rising as shown in
Figure 3.
iv.
Observe the value of T2T1 on the scope, which is the one time constant, as shown below.
v.
Record the result in
Table 1 above under measured value using VC.
Figure 5: Measuring RC time constant using VC
9.
Connect Channel B of the oscilloscope across the resistor.
10. You should be able to see the waveform as shown below. (Use Volts/Div and Time/DIV knobs to adjust the signal)
Figure 6(a): Voltage across the resistor
11.
Measuring the time constant with VR:
i.
Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ___5 v______.
ii.
Calculate the 37% of the above value ___1.85 V______.
iii. Place the second cursor (T2) at the step (ii) value above.
iv. Observe the T2T1 value on the scope, which is the one time constant.
v.
Record the result in
Table 1under measured value using VR.
Figure 6(b): Measuring RC timeconstant using VR
Part II:
12.
Place two capacitors in series as shown in
Figure 7 below.
Figure 7: Series Capacitors
13.
Calculate the total capacitance value and
record the results in
Table 2 below.
Calculated Value 
Measured Value 

Capacitance 
11µF 
10.2µF 
Table 2: Series Capacitors
14.
Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.
i.
Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter) as shown in
Figure 8.
ii.
Measure the capacitive reactance, XC, as shown in
Figure 8.
iii.
Calculate the capacitance using the equation, and
record the value in
Table 2.
Figure 8: Impedance Meter in Multisim
15.
Modify the circuit as shown below, by placing two 0.22µF capacitors in series as in
Figure 8.
Figure 8: RC circuit with two series capacitors
16.
Calculate the new RC time constant using measured values.
Record the result in
Table 3 below.
Calculated value
Measured value using VR
Time constant ()
114.653 us
Table 3: Calculated and measured values
17.
Connect Channel A of the oscilloscope across the resistor
18. Adjust the trigger if needed, and you should be able to see the waveform as shown in
Figure 9 below.
Figure 9: Voltage Across the Resistor
19.
Repeat step 11.
Record the measured time constant in
Table 3 above.
Part III:
20.
Place two capacitors in parallel as shown in
Figure 10 below. (
Note: The 0.001 Ω resistor is
ONLY required for simulation in Multisim. Without the resistor, the mathematical model will not converge).
Figure 10: Parallel Capacitors
21.
Calculate the total capacitance value and
record the results in
Table 4 below.
Calculated Value
Measured Value
Capacitance
0.44µF
0.442µF
Table 4: Parallel Capacitors
22.
Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.
i.
Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter).
ii.
Measure the capacitive reactance.
iii.
Calculate the capacitance using the equation, and
record the value in
Table 4.
23.
Modify the circuit by placing two 0.22µF capacitors in parallel as in
Figure 11.
Figure 11: RC Circuit with Parallel Capacitors
24.
Calculate the new RC time constant using measured values.
Record the result in
Table 5 below.
25.
Connect Channel A of the oscilloscope across the resistor.
26. You should be able to see the waveform as in
Figure 12 below. (Use Volts/Div and Time/DIV knobs to adjust the signal)
27. Use the cursors on the oscilloscope to
measure the time constant (refer to step 11).
Record the result in
Table 5 below under measured value.
Figure 12: Voltage across the resistor
Calculated value
Measured value using VR
Time constant ()
458.611us
Table 5: Calculated and measured values
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ELECTRIC CIRCUITS I
METRIC PREFIX TABLE
Metric
Prefix
Symbol
Multiplier
(Traditional Notation)
Expo
nential
Description
Yotta
Y
1,000,000,000,000,000,000,000,000
1024
Septillion
Zetta
Z
1,000,000,000,000,000,000,000
1021
Sextillion
Exa
E
1,000,000,000,000,000,000
1018
Quintillion
Peta
P
1,000,000,000,000,000
1015
Quadrillion
Tera
T
1,000,000,000,000
1012
Trillion
Giga
G
1,000,000,000
109
Billion
Mega
M
1,000,000
106
Million
kilo
k
1,000
103
Thousand
hecto
h
100
102
Hundred
deca
da
10
101
Ten
Base
b
1
100
One
deci
d
1/10
101
Tenth
centi
c
1/100
102
Hundredth
milli
m
1/1,000
103
Thousandth
micro
µ
1/1,000,000
106
Millionth
nano
n
1/1,000,000,000
109
Billionth
pico
p
1/1,000,000,000,000
1012
Trillionth
femto
f
1/1,000,000,000,000,000
1015
Quadrillionth
atto
a
1/1,000,000,000,000,000,000
1018
Quintillionth
zepto
z
1/1,000,000,000,000,000,000,000
1021
Sextillionth
yocto
y
1/1,000,000,000,000,000,000,000,000
1024
Septillionth
4BAND RESISTOR COLOR CODE TABLE
BAND
COLOR
DIGIT
Band 1: 1st Digit
Band 2: 2nd Digit
Band 3: Multiplier
(# of zeros
following 2nd digit)
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
Band 4: Tolerance
Gold
± 5%
SILVER
± 10%
5BAND RESISTOR COLOR CODE TABLE
BAND
COLOR
DIGIT
Band 1: 1st Digit
Band 2: 2nd Digit
Band 3: 3rd Digit
Band 4: Multiplier
(# of zeros
following 3rd digit)
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
Gold
0.1
SILVER
0.01
Band 5: Tolerance
Gold
± 5%
SILVER
± 10%
EET Formulas & Tables Sheet
Page
1 of
21
UNIT 1: FUNDAMENTAL CIRCUITS
CHARGE
Where:
Q = Charge in Coulombs (C)
Note:
1 C = Total charge possessed by 6.25×1018 electrons
VOLTAGE
Where:
V = Voltage in Volts (V)
W = Energy in Joules (J)
Q = Charge in Coulombs (C)
CURRENT
Where:
I = Current in Amperes (A)
Q = Charge in Coulombs (C)
t = Time in seconds (s)
OHM’S LAW
Where:
I = Current in Amperes (A)
V = Voltage in Volts (V)
R = Resistance in Ohms (Ω)
RESISTIVITY
Where:
ρ = Resistivity in Circular Mil – Ohm per Foot (CMΩ/ft)
A = Crosssectional area in Circular Mils (CM)
R = Resistance in Ohms (Ω)
ɭ = Length in Feet (ft)
Note:
CM: Area of a wire with a 0.001 inch (1 mil) diameter
CONDUCTANCE
Where:
G = Conductance in Siemens (S)
R = Resistance in Ohms (Ω)
CROSSSECTIONAL AREA
Where:
A = Crosssectional area in Circular Mils (CM)
d = Diameter in thousandths of an inch (mils)
ENERGY
Where:
W = Energy in Joules (J). Symbol
is an italic
W.
P = Power in Watts (W). Unit
is not an italic W.
t = Time in seconds (s)
Note:
1 W = Amount of power when 1 J of energy
is used in 1 s
POWER
Where:
P = Power in Watts (W)
V
= Voltage in Volts (V)
I = Current in Amperes (A)
Note:
Ptrue = P in a resistor is also called true power
OUTPUT POWER
Where:
POUT = Output power in Watts (W)
PIN = Input power in Watts (W)
PLOSS = Power loss in Watts (W)
POWER SUPPLY EFFICIENCY
Where:
POUT = Output power in Watts (W)
PIN = Input power in Watts (W)
Efficiency = Unitless value
Note:
Efficiency expressed as a percentage:
UNIT 2: SERIES CIRCUITS (R1, R2, , Rn)
TOTAL RESISTANCE
Where:
RT = Total series resistance in Ohms (Ω)
Rn
= Circuit’s last resistor in Ohms (Ω)
KIRCHHOFF’S VOLTAGE LAW
Where:
VS = Voltage source in Volts (V)
Vn = Circuit’s last voltage drop in Volts (V)
VOLTAGE – DIVIDER
Where:
Vx = Voltage drop in Ohms (Ω)
Rx
= Resistance where Vx occurs in Ohms (Ω)
RT = Total series resistance in Ohms (Ω)
VS
= Voltage source in Volts (V)
TOTAL POWER
Where:
PT = Total power in Watts (W)
Pn = Circuit’s last resistor’s power in Watts (W)
UNIT 3: PARALLEL CIRCUITS (R1R2Rn)
TOTAL RESISTANCE
Where:
RT = Total parallel resistance in Ohms (Ω)
Rn
= Circuit’s last resistor in Ohms (Ω)
TOTAL RESISTANCE – TWO RESISTORS IN PARALLEL
Where:
RT = Total parallel resistance in Ohms (Ω)
TOTAL RESISTANCE – EQUALVALUE RESISTORS
Where:
RT = Total parallel resistance in Ohms (Ω)
R = Resistor Value in Ohms (Ω)
n = Number of equal value resistors (Unitless)
UNKNOWN RESISTOR
Where:
Rx = Unknown resistance in Ohms (Ω)
RA = Known parallel resistance in Ohms (Ω)
RT = Total parallel resistance in Ohms (Ω)
KIRCHHOFF’S CURRENT LAW
Where:
n = Number of currents into node (Unitless)
m = Number of currents going out of node (Unitless)
CURRENT – DIVIDER
Where:
Ix = Branch “x” current in Amperes (A)
RT = Total parallel resistance in Ohms (Ω)
Rx = Branch “x” resistance in Ohms (Ω)
IT = Total current in Amperes (A)
TWOBRANCH CURRENT – DIVIDER
Where:
I1 = Branch “1” current in Amperes (A)
R2 = Branch “2” resistance in Ohms (Ω)
R1 = Branch “1” resistance in Ohms (Ω)
IT = Total current in Amperes (A)
TOTAL POWER
Where:
PT = Total power in Watts (W)
Pn = Circuit’s last resistor’s power in Watts (W)
OPEN BRANCH RESISTANCE
Where:
ROpen = Resistance of open branch in Ohms (Ω)
RT(Meas) = Measured resistance in Ohms (Ω)
GT(Calc) = Calculated total conductance in Siemens (S)
GT(Meas) = Measured total conductance in Siemens (S)
Note:
GT(Meas) obtained by measuring total resistance, RT(Meas)
UNIT 4: SERIES – PARALLEL CIRCUITS
BLEEDER CURRENT
Where:
IBLEEDER = Bleeder current in Amperes (A)
IT = Total current in Amperes (A)
IRL1 = Load resistor 1 current in Amperes (A)
IRL2 = Load resistor 2 current in Amperes (A)
THERMISTOR BRIDGE OUTPUT
Where:
= Change in output voltage in Volts (V)
= Change in thermal resistance in Ohms (Ω)
VS = Voltage source in Volts (V)
R = Resistance value in Ohms (Ω)
UNKNOWN RESISTANCE IN A WHEATSTONE BRIDGE
Where:
RX = Unknown resistance in Ohms (Ω)
RV = Variable resistance in Ohms (Ω)
R2 = Resistance 2 in Ohms (Ω)
R4 = Resistance 4 in Ohms (Ω)
UNIT 5: MAGNETISM AND ELECTROMAGNETISM
MAGNETIC FLUX DENSITY
Where:
B = Magnetic flux density in Tesla (T)
= Flux in Weber (Wb)
(Greek letter Phi)
A = Crosssectional area in square meters (m2)
Note:
Tesla (T) equals a Weber per square meter (Wb/m2)
RELATIVE PERMEABILITY
Where:
= Relative permeability (Unitless)
(Greek letter Mu)
= Permeability in Webers per Ampereturn · meter
(Wb/At·m)
= Vacuum permeability in Webers per Ampere
turn · meter (Wb/At·m)
Note:
= Wb/ At·m
RELUCTANCE
Where:
R = Reluctance in Ampereturn per Weber (At/Wb)
ɭ = Length of magnetic path in meters (m)
µ = Permeability in Weber per Ampereturn · meter
(Wb/At · m)
A = Crosssectional area in meters squares (m2)
MAGNETOMOTIVE FORCE
Where:
Fm = Magnetomotive force (mmf) in Ampereturn (At)
N
= Number of Turns of wire (t)
I = Current in Amperes (A)
MAGNETIC FLUX
Where:
= Flux in Weber (Wb)
Fm = Magnetomotive force in Ampereturn (At)
R = Reluctance in Ampereturn per Weber (At/Wb)
MAGNETIC FIELD INTENSITY
Where:
H = Magnetic field intensity in Amperesturn per
meter (At/m)
Fm = Magnetomotive force in Ampereturn (At)
ɭ = Length of material in meters (m)
INDUCED VOLTAGE
Where:
vind = Induced voltage in Volts (V)
B = Magnetic flux density in Tesla (T)
ɭ = Length of the conductor exposed to the magnetic
field in meters (m)
v = Relative velocity in meters per second (m/s)
Note:
Tesla (T) equals a Weber per square meter (Wb/m2)
FARADAY’S LAW
Where:
vind = Induced voltage in Volts (V)
N = Number of turns of wire in the coil (Unitless)
= Rate of change of magnetic field with respect
to the coil in Webers per second (Wb/s)
ELECTRIC CIRCUITS II
UNIT 1: ALTERNATE CURRENT & INDUCTORS
ALTERNATE CURRENT
FREQUENCY & PERIOD
Where:
f = Frequency in Hertz (Hz)
T = Period in Seconds (s)
Note:
1 Hertz = 1 cycle per 1 second
PEAK TO PEAK VOLTAGE
Where:
Vpp = Peak to peak voltage in Volts (V)
Vp = Peak voltage in Volts (V)
ROOT MEAN SQUARE (RMS) VOLTAGE
Where:
Vrms = Root mean square voltage in Volts (V)
Vp = Peak voltage in Volts (V)
HALFCYCLE AVERAGE VOLTAGE
Where:
Vavg = Halfcycle average voltage in Volts (V)
Vp = Peak voltage in Volts (V)
RADIAN & DEGREE CONVERSION
Where:
Rad = Number of radians in Rad (rad)
Degrees = Number of degrees in Degrees (0)
Note:
= 3.1416 (Greek letter Pi)
GENERATOR OUTPUT FREQUENCY
Where:
f = Frequency in Hertz (Hz)
Number of pole pairs = Number of pole pairs (Unitless)
rps = Revolutions per second in Revolutions per
Second (rps)
PEAK TO PEAK CURRENT
Where:
Ipp = Peak to peak current in Amperes (A)
Ip = Peak current in Amperes (A)
ROOT MEAN SQUARE (RMS) CURRENT
Where:
Irms = Root mean square current in Amperes (A)
Ip = Peak current in Amperes (A)
HALFCYCLE AVERAGE CURRENT
Where:
Iavg = Halfcycle average current in Amperes (A)
Ip = Peak current in Amperes (A)
SINE WAVE GENERAL FORMULA
Where:
y = Instantaneous voltage or current value
at angle in Volts or Amperes (V or A)
(Greek letter Theta)
A = Maximum voltage or current value in Volts or
Amperes (V or A)
= Angle where given instantaneous voltage or
current value exists
SINE WAVE LAGGING THE REFERENCE
Where:
y = Instantaneous voltage or current value
at angle in Volts or Amperes (V or A)
A = Maximum voltage or current value in Volts or
Amperes (V or A)
= Angle where given instantaneous voltage or
current value exists
= Angle sine wave is shifted right (lagging) of
reference (Greek letter Phi)
ANGULAR VELOCITY
Where:
= Angular velocity in Radians per second (rad/s)
(Small Greek letter omega)
f = Frequency in Hertz (Hz)
Note:
= 3.1416
SINE WAVE VOLTAGE
Where:
v = Sinusoidal voltage in Volts (V)
Vp = Peak voltage in Volts (V)
f = Frequency in Hertz (Hz)
t = Time in Seconds (s)
Note:
= 3.1416
PULSE WAVEFORM AVERAGE VALUE
Where:
vavg = Pulse waveform average value in Volts (V)
baseline = Baseline in Volts (V)
duty cycle = Percent duty cycle in Percent/100%
(Unitless)
Amplitude = Amplitude in Volts (V)
SINE WAVE LEADING THE REFERENCE
Where:
y = Instantaneous voltage or current value
at angle in Volts or Amperes (V or A)
A = Maximum voltage or current value in Volts or
Amperes (V or A)
= Angle where given instantaneous voltage or
current value exists
= Angle sine wave is shifted left (leading) of
reference
PHASE ANGLE
Where:
= Angle sine wave is shifted in Radians (rad)
= Angular velocity in Radians per second (rad/s)
t = Time in Seconds (s)
DUTY CYCLE
Where:
Percent duty cycle = Percent duty cycle in Percentage (%)
tw = Pulse width in Seconds (s)
T = Period in Seconds (s)
F = Frequency in Hertz (Hz)
INDUCTORS
INDUCED VOLTAGE
Where:
vind = Induced voltage in Volts (V)
L = Inductance in Henries (H)
= Time rate of change of the current in Amperes
per second (A/s)
INDUCTANCE OF A COIL
Where:
L = Inductance of a coil in Henries (H)
N = Number of turns of wire (Unitless)
= Permeability in Henries per meter (H/m)
A = Crosssectional area in Meters squared (m2)
= Core length in Meters (m)
Notes:
Permeability in H/m is equal to Wb/At·m
Nonmagnetic core = Permeability of a vacuum, µ0
µ0 = 4 x 107 H/m
RL TIME CONSTANT
Where:
= RL time constant in Seconds (s) (Greek letter Tau)
L = Inductance in Henries (H)
R = Resistance in Ohms (Ω)
GENERAL EXPONENTIAL VOLTAGE FORMULA
Where:
v = Instantaneous voltage at time, t, in Volts (V)
VF = Voltage final value in Volts (V)
Vi = Voltage initial value in Volts (V)
R = Resistance in Ohms (Ω)
t = Time in Seconds (s)
L = Inductance in Henries (H)
INDUCTOR ENERGY STORAGE
Where:
W = Energy in Joules (J)
L = Inductance in Henries (H)
I = Current in Amperes (A)
TOTAL INDUCTANCE – SERIES
Where:
LT = Total series inductance in Henries (H)
Ln = Circuit’s last inductor in Henries (H)
TOTAL INDUCTANCE – PARALLEL
Where:
LT = Total parallel inductance in Henries (H)
Ln
= Circuit’s last inductor in Henries (H)
RL CIRCUIT CURRENT INCREASE AND DECREASE
FOR GIVEN NUMBER OF TIME CONSTANTS
# of Time Constants
Approx % of Final Current
Approx % of Initial Charge
1
63
37
2
86
14
3
95
5
4
98
2
5
99
Considered 100%
1
Considered 0%
GENERAL EXPONENTIAL CURRENT FORMULA
Where:
i = Instantaneous current at time, t, in Amperes (A)
IF = Current final value in Amperes (A)
Ii = Current initial value in Amperes (A)
R = Resistance in Ohms (Ω)
t = Time in Seconds (s)
L = Inductance in Henries (H)
INDUCTIVE REACTANCE
Where:
XL = Inductive reactance in Ohms (Ω)
f = Frequency in Hertz (Hz)
L = Inductance in Henries (H)
Note:
= 3.1416 (Greek letter “Pi”)
INDUCTOR REACTIVE POWER
Where:
Pr = Reactive Power in Watts (W)
Vrms = Voltage rms in Volts (V)
Irms = Current rms in Amperes (A)
XL = Inductive reactance in Ohms (Ω)
UNIT 2: RL CIRCUITS
SERIES RL CIRCUIT
IMPEDANCE IN RECTANGULAR FORM
Where:
Z = Impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
Note:
Bold letters represent complete phasor quantities.
For example, “
Z” in the formula above
VOLTAGE IN RECTANGULAR FORM
Where:
Vs = Voltage in Volts (V)
VR = Resistor voltage in Volts (V)
VL = Inductor voltage in Volts (V)
INDUCTOR TRUE POWER
Where:
Ptrue = True Power in Watts (W)
Irms = Current rms in Amperes (A)
RW = Winding resistance in Ohms (Ω)
COIL QUALITY FACTOR
Where:
Q = Coil quality factor (Unitless)
XL = Inductive reactance in Ohms (Ω)
RW = Winding resistance of the coil or the resistance
in series with the coil in Ohms (Ω)
Note:
Circuit Q and the coil Q are the same when the resistance is only the coil winding resistance
IMPEDANCE IN POLAR FORM
Where:
Z = Impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
Note:
= Magnitude
= Phase Angle
VOLTAGE IN POLAR FORM
Where:
Vs = Voltage in Volts (V)
VR = Resistor voltage in Volts (V)
VL = Inductor voltage in Volts (V)
LEAD CIRCUIT
ANGLE BETWEEN VOLTAGE IN & OUT
Where:
= Angle between voltage in and out in Degrees (0)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
OUTPUT VOLTAGE MAGNITUDE
Where:
Vout = Voltage output in Volts (V)
XL = Inductive reactance in Ohms (Ω)
R = Resistance in Ohms (Ω)
LAG CIRCUIT
ANGLE BETWEEN VOLTAGE IN & OUT
Where:
= Angle between voltage in and out in Degrees (0)
XL = Inductive reactance in Ohms (Ω)
R = Resistance in Ohms (Ω)
OUTPUT VOLTAGE MAGNITUDE
Where:
Vout = Output voltage in Volts (V)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
Vin = Input voltage in Volts (V)
PARALLEL RL CIRCUIT
TOTAL 2COMPONENT IMPEDANCE
Where:
Z = Total 2component impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
CURRENT IN POLAR FORM
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IL = Inductor current in Amperes (A)
TOTAL ADMITTANCE
Where:
Y = Total admittance in Siemens (S)
G = Conductance in Siemens (S)
BL = Inductive Susceptance in Siemens (S)
Note:
CURRENT IN RECTANGULAR FORM
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IL = Inductor current in Amperes (A)
PARALLEL TO SERIES FORM CONVERSION
Where:
Req = Resistance in Ohms (Ω)
Z = Impedance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
= Angle where given instantaneous voltage or
current value exists
POWER
RL CIRCUIT REACTIVE POWER
Where:
Pr = Reactive power in VoltAmpere Reactive (VAR)
Itot = Total current in Amperes (A)
XL = Inductive reactance in Ohms (Ω)
UNIT 3: CAPACITORS
CAPACITANCE
Where:
C = Capacitance in Farads (F)
Q = Charge in Coulombs (C)
V = Voltage in Volts (V)
ENERGY STORED IN A CAPACITOR
Where:
W = Energy in Joules (J)
C = Capacitance in Farads (F)
V = Voltage in Volts (V)
DIELECTRIC CONSTANT (RELATIVE PERMITTIVITY)
Where:
= Dielectric constant (Unitless)
(Greek letter Epsilon)
= Absolute permittivity of a material in Farads per
meter (F/m)
= Absolute permittivity of a vacuum in Farads per
meter (F/m)
Note:
= 8.85 x 1012 F/m
CAPACITANCE
Where:
C = Capacitance in Farads (F)
A = Plate area in Meters squared (m2)
= Dielectric constant (Unitless)
d = Plate separation in Meters (m)
Note:
If d is in mils, 1 mil = 2.54 x 105 meters
SERIES CAPACITORS
TOTAL CHARGE
Where:
QT = Total charge in Coulombs (C)
Qn = Circuit’s last capacitor charge in Coulombs (C)
TOTAL CAPACITANCE
Where:
CT = Total series capacitance in Farads (F)
Cn
= Circuit’s last capacitor’s capacitance in
Farads (F)
TOTAL CAPACITANCE – TWO CAPACITORS
Where:
CT = Total series capacitance in Farads (F)
VOLTAGE ACROSS A CAPACITOR
Where:
Vx = Voltage drop in Volts (V)
CT = Total series capacitance in Farads (F)
Cx = Capacitor x’s capacitance in Farads (F)
VT = Total voltage in Volts (V)
TOTAL CAPACITANCE – EQUALVALUE CAPACITORS
Where:
CT = Total series capacitance in Farads (F)
n = Number of equal value capacitors (Unitless)
PARALLEL CAPACITORS
TOTAL CHARGE
Where:
QT = Total charge in Coulombs (C)
Qn = Circuit’s last capacitor charge in Coulombs (C)
TOTAL CAPACITANCE – EQUALVALUE CAPACITORS
Where:
CT = Total series capacitance in Farads (F)
n = Number of equal value capacitors (Unitless)
CAPACITORS IN DC CIRCUITS
RC TIME CONSTANT
Where:
= Time constant in Seconds (s)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
TOTAL CAPACITANCE
Where:
CT = Total series capacitance in Farads (F)
Cn
= Circuit’s last capacitor’s capacitance in
Farads (F)
RC CIRCUIT CURRENT INCREASE AND DECREASE
FOR GIVEN NUMBER OF TIME CONSTANTS
# of Time Constants
Approx % of Final Current
Approx % of Initial Charge
1
63
37
2
86
14
3
95
5
4
98
2
5
99
Considered 100%
1
Considered 0%
GENERAL EXPONENTIAL VOLTAGE FORMULA
Where:
v = Instantaneous voltage at time, t, in Volts (V)
VF = Voltage final value in Volts (V)
Vi = Voltage initial value in Volts (V)
t = Time in Seconds (s)
= Time constant in Seconds (s)
CHARGING TIME TO A SPECIFIED VOLTAGE
Where:
t = Time in Seconds (s)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
v = Specified voltage level in Volts (V)
VF = Final voltage level in Volts (V)
Note:
Assumes Vi = 0 Volts
GENERAL EXPONENTIAL CURRENT FORMULA
Where:
i = Instantaneous current at time, t, in Amperes (A)
IF = Current final value in Amperes (A)
Ii = Current initial value in Amperes (A)
t = Time in Seconds (s)
= Time constant in Seconds (s)
DISCHARGING TIME TO A SPECIFIED VOLTAGE
Where:
t = Time in Seconds (s)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
v = Specified voltage level in Volts (V)
Vi = Initial voltage level in Volts (V)
Note:
Assumes VF = 0 Volts
CAPACITORS IN AC CIRCUITS
INSTANTANEOUS CAPACITOR CURRENT
Where:
i = Instantaneous current in Amperes (A)
C = Capacitance in Farads (F)
= Instantaneous rate of change of the voltage
across the capacitor in Volts per second (V/s)
CAPACITOR REACTIVE POWER
Where:
Pr = Reactive Power in VoltAmpere Reactive (VAR)
Vrms = Voltage rms in Volts (V)
Irms = Current rms in Amperes (A)
XC = Capacitive reactance in Ohms (Ω)
CAPACITIVE REACTANCE
Where:
XC = Capacitive reactance in Ohms (Ω)
f = Frequency in Hertz (Hz)
C = Capacitance in Farads (F)
Note:
= 3.1416 (Greek letter “Pi”)
SWITCHEDCAPACITORS CIRCUITS
AVERAGE CURRENT
Where:
I1(avg) = Instantaneous current in Amperes (A)
C = Capacitance in Farads (F)
V1 = Voltage 1 in Volts (V)
V2 = Voltage 2 in Volts (V)
T = Period of time in Seconds (s)
UNIT 4: RC CIRCUITS
RC SERIES CIRCUITS
IMPEDANCE IN RECTANGULAR FORM
Where:
Z = Impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
OHM’S LAW
Where:
I = Current in Amperes (A)
Z = Impedance in Ohms (Ω)
V = Voltage in Volts (V)
VOLTAGE IN RECTANGULAR FORM
Where:
Vs = Voltage in Volts (V)
VR = Resistor voltage in Volts (V)
VC = Capacitor voltage in Volts (V)
LEAD CIRCUIT
ANGLE BETWEEN VOLTAGE IN & OUT
Where:
= Angle between voltage in and out in Degrees (0)
XC = Capacitive reactance in Ohms (Ω)
R = Resistance in Ohms (Ω)
EQUIVALENT RESISTANCE
Where:
R = Equivalent resistance in Ohms (Ω)
T = Period of time in Seconds (s)
C = Capacitance in Farads (F)
f = Frequency in Hertz (Hz)
IMPEDANCE IN POLAR FORM
Where:
Z = Impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
VOLTAGE IN POLAR FORM
Where:
Vs = Voltage in Volts (V)
VR = Resistor voltage in Volts (V)
VC = Capacitor voltage in Volts (V)
OUTPUT VOLTAGE MAGNITUDE
Where:
Vout = Voltage output in Volts (V)
R = Resistance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
LAG CIRCUIT
ANGLE BETWEEN VOLTAGE IN & OUT
Where:
= Angle between voltage in and out in Degrees (0)
R = Resistance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
RC PARALLEL CIRCUITS
TOTAL 2COMPONENT IMPEDANCE
Where:
Z = Total 2component impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
OHM’S LAW
Where:
I = Current in Amperes (A)
V = Voltage in Volts (V)
Y = Admittance in Siemens (S)
CURRENT IN RECTANGULAR FORM
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IC = Capacitor current in Amperes (A)
PARALLEL TO SERIES FORM CONVERSION
Where:
Req = Resistance in Ohms (Ω)
Z = Impedance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
= Angle where given instantaneous voltage or
current value exists
OUTPUT VOLTAGE MAGNITUDE
Where:
Vout = Voltage output in Volts (V)
XC = Capacitive reactance in Ohms (Ω)
R = Resistance in Ohms (Ω)
TOTAL ADMITTANCE
Where:
Y = Total admittance in Siemens (S)
G = Conductance in Siemens (S)
BC = Capacitive susceptance in Siemens (S)
Note:
CURRENT IN POLAR FORM
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IC = Capacitor current in Amperes (A)
RC SERIES –PARALLEL CIRCUITS
PHASE ANGLE
Where:
Req = Resistance in Ohms (Ω)
Z = Impedance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
= Angle where given instantaneous voltage or
current value exists
POWER
APPARENT POWER
Where:
Pa = Apparent power in Voltampere (VA)
I = Current in Amperes (A)
Z = Impedance in Ohms (Ω)
POWER FACTOR
Where:
PF = Power Factor (Unitless)
= Phase angle in Degrees (0)
OSCILLATOR AND FILTER
OSCILLATOR OUTPUT FREQUENCY
Where:
fr = Output frequency in Hertz (Hz)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
Note:
= 3.1416
UNIT 5: RLC CIRCUITS AND PASSIVE FILTERS
RLC SERIES CIRCUITS
TOTAL REACTANCE
Where:
Xtot = Total reactance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
TOTAL IMPEDANCE IN POLAR FORM
Where:
Z = Total impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
Xtot = Total reactance in Ohms (Ω)
Note:
When XL > XC, the angle is positive
When XC > XL, the angle is negative
TRUE POWER
Where:
Ptrue = True power in Watts (W)
V = Voltage in Volts (V)
I = Current in Amperes (A)
= Phase angle in Degrees (0)
FILTER CUTOFF FREQUENCY
Where:
fc = Cutoff frequency in Hertz (Hz)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
Note:
= 3.1416
TOTAL IMPEDANCE IN RECTANGULAR FORM
Where:
Z = Total impedance in Ohms (Ω)
R = Resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
XC = Capacitive reactance in Ohms (Ω)
RESONANT FREQUENCY
Where:
fr = Resonant frequency in Hertz (Hz)
L = Inductance in Henries (H)
C = Capacitance in Farads (F)
Note:
At resonance, XL = XC and the j terms cancel
= 3.1416
RLC PARALLEL CIRCUITS
TOTAL CURRENT
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IC = Capacitor current in Amperes (A)
IL = Inductor current in Amperes (A)
ICL = Total current into the L and C branches
in Amperes (A)
RLC PARALLEL RESONANCE
RESONANT FREQUENCY – IDEAL
Where:
fr = Resonant frequency in Hertz (Hz)
L = Inductance in Henries (H)
C = Capacitance in Farads (F)
Note:
At resonance, XL = XC and Zr =
= 3.1416
CURRENT AND PHASE ANGLE
Where:
Itot = Total current in Amperes (A)
VS = Voltage source in Volts (V)
Zr = Impedance at resonance in Ohms (Ω)
RESONANT FREQUENCY – PRECISE
Where:
fr = Resonant frequency in Hertz (Hz)
RW = Winding resistance in Ohms (Ω)
C = Capacitance in Farads (F)
L = Inductance in Henries (H)
Note:
= 3.1416
RLC SERIES – PARALLEL CIRCUITS
SERIESPARALLEL TO PARALLEL CONVERSION
EQUIVALENT INDUCTANCE
Where:
Leq = Equivalent inductance in Henries (H)
L = Inductance in Henries (H)
Q = Coil quality factor (Unitless)
EQUIVALENT PARALLEL RESISTANCE
Where:
Rp(eq) = Equivalent parallel resistance in Ohms (Ω)
RW = Winding resistance in Ohms (Ω)
Q = Coil quality factor (Unitless)
NONIDEAL TANK CIRCUIT
TOTAL IMPEDANCE AT RESONANCE
Where:
ZR = Total impedance in Ohms (Ω)
RW = Resistance in Ohms (Ω)
Q = Coil quality factor (Unitless)
SPECIAL TOPICS
RESONANT CIRCUIT BANDWIDTH
BANDWIDTH
Where:
BW = Bandwidth in Hertz (Hz)
f2 = Upper critical frequency at Z=0.707·Zmax
in Hertz (Hz)
f1 = Lower critical frequency at Z=0.707·Zmax
in Hertz (Hz)
BANDWIDTH AND QUALTIY FACTOR
Where:
BW = Bandwidth in Hertz (Hz)
fr = Center (resonant) frequency in Hertz (Hz)
Q = Coil quality factor (Unitless)
PASSIVE FILTERS
POWER RATIO IN DECIBELS
Where:
dB = Power ratio in decibels (dB)
Pout = Output power in Watts (W)
Pin = Input power in Watts (W)
OVERALL QUALITY FACTOR WITH AN EXTERNAL LOAD
Where:
QO = Overall quality factor (Unitless)
Rp(tot)= Total parallel equivalent resistance in Ohms (Ω)
XL = Inductive reactance in Ohms (Ω)
CENTER (RESONANT) FREQUENCY
Where:
fr = Center (resonant) frequency in Hertz (Hz)
f1 = Lower critical frequency at Z=0.707·Zmax
in Hertz (Hz)
f2 = Upper critical frequency at Z=0.707·Zmax
in Hertz (Hz)
VOLTAGE RATIO IN DECIBELS
Where:
dB = Power ratio in decibels (dB)
Vout = Output voltage in Volts (V)
Vin = Input voltage in Volts (V)
LOWPASS & HIGHPASS FILTERS
RC FILTERS
Where:
fC = Filter critical frequency in Hertz (Hz)
R = Resistance in Ohms (Ω)
C = Capacitance in Farads (F)
Note:
= 3.1416
At fC, Vout = (0.707)·Vin
SERIES RESONANT BANDPASS FILTER
Where:
BW = Bandwidth in Hertz (Hz)
f0 = Center frequency in Hertz (Hz)
Q = Coil quality factor (Unitless)
RL FILTERS
Where:
fc = Filter critical frequency in Hertz (Hz)
L = Inductance in Henries (H)
R = Resistance in Ohms (Ω)
Note:
= 3.1416
At fC, Vout = (0.707)·Vin
GENERAL INFORMATION
AREA AND VOLUMES
AREAS
CIRCLE AREA
Where:
A = Circle area in meters squared (m2)
r = Radius in meters (m)
Note:
= 3.1416
RECTANGULAR AND POLAR FORMS
RECTANGULAR FORM
Where:
A = Coordinate value on real axis (Horizontal Plane)
j = j operator
B = Coordinate value on imaginary axis (Vertical Plan)
Note:
“j operator” prefix indicates designated coordinate value is on imaginary axis.
COMPLEX PLANE AND RECTANGULAR FORM PHASOR
+A
Quadrant 1
Quadrant 3
Quadrant 4
A
+jB
jB
(A + jB)
(A – jB)
(A + jB)
(A – jB)
Quadrant 2
00/3600
1800
900
2700
POLAR FORM
Where:
C = Phasor magnitude
= Phasor angle relative to the positive real axis
COMPLEX PLANE AND POLAR FORM PHASOR
Real Axis
Quadrant 1
Quadrant 3
Quadrant 4
+j
j
Length = Magnitude
–
Quadrant 2
+
RECTANGULAR TO POLAR CONVERSION
Where:
A = Coordinate value on real axis (Horizontal Plane)
j = j operator
B = Coordinate value on imaginary axis (Vertical Plan)
C = Phasor magnitude
= Phasor angle relative to the positive real axis
Note:
To calculate C:
To calculate in Quadrants 1 and 4 (A is positive):
Use +B for +B values, B for –B values
To calculate in Quadrants 2 and 3 (A is negative):
Use for +B values
Use for –B values
POLAR TO RECTANGULAR CONVERSION
Where:
C = Phasor magnitude
= Phasor angle relative to the positive real axis
A = Coordinate value on real axis (Horizontal Plane)
j = j operator
B = Coordinate value on imaginary axis (Vertical Plan)
Note:
To calculate A:
To calculate B:
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