Fundamentals Of Electricity. Simple DC Series Circuit, . R t = R 1 +R 2 +R 3. Simple DC Parallel Circuit, . R t = (R 1 .R 2 .R 3 ) /(R 2 .R 1 +R 3 .R 2 +R 1 .R 3 ) . Fundamentals Of Electricity. Simple AC Series Circuit, . Simple AC Parallel Circuit, . Fundamentals Of Electricity.
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Simple DC Series Circuit,
Rt = R1+R2+R3
Simple DC Parallel Circuit,
Rt = (R1.R2.R3 ) /(R2.R1+R3.R2+R1 .R3)
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Simple AC Series Circuit,
Simple AC Parallel Circuit,
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Three Phase (AC) Transformer Configurations
Note:
a = Turns Ratio = Np/Ns
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Impedance:
Z = R + jXl  jXc
Where, jXl = Zl and, jXc =Zc
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Ohms Law:
V= I Rfor DC circuits
V = I Z for AC Circuits
Note:BOLD letters, in general, represent Vectoral quantities
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Power :
Papparent= S= Apparent Power (kVA) or Total AC Power
Preal = P = Real Power Comp. of Apparent Power, in kW
Preactive= Q = Reactive Comp. of App. Power in kVAR
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Power Factor :
PF = P/S or
PF = cos(  ),
Note:Detailed discussion on the topic of Power Factor is covered under the Power Factor segment of this seminar.
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Voltage Regulation:
Definition: Real voltage sources are unable to hold the voltage constant as they assume a significant amount of load (Resistance or Impedance). This results in the difference between Vno load and Vfull load.
The formula for Voltage Regulation is as follows:
Voltage Reg. = (Vno load  Vfull load)/ Vfull load x 100%
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Service Factor of a Motor:
Definition: Service factor of a motor is the ratio of safe to standard (nameplate) loads. Service factor is expressed in decimal. The formula for Service Factor is as follows:
Service Factor = Safe Load / Nameplate Load
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Classifications of Motors:
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Classifications of Motors, contd.:
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Kirchhoff’s Voltage Law (KVL):
Algebraic sum of voltage drops around any closed path, within a circuit, is equal to the sum of voltages presented by all of the voltage sources. The mathematical representation of KVL is as follows:
VDrops = VSource
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Kirchhoff’s Current Law (KCL):
Total current flowing into a node is equal to the total current that flows out of the node. The mathematical representation of KCL is as follows:
iin = iout
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Motor Speed Calculation:
Number of Poles = P = 4
Frequency of AC Power Supply to the Motor, in Hertz = f = 60 Hz
Speed, in RPM = S = ?
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Motor Slip:
Slip is usually expressed in percent and can be computed as follows:
Percent slip = (Synchronous speed  Actual speed ) x 100
Synchronous Speed
The direction of rotation of a polyphase ac induction motor depends on the connection of the stator leads to the power lines. Interchanging any two input leads reverses rotation.
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Motor Torque, Power and Horsepower:
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Motor Torque and Horsepower, contd.:
Torque(ftlbf) = 5250 x P (horsepower)
Speed(rpm)
Torque(Nm) = 9549 x P (kW)
Speed(rpm)
Electrical Engineering Fundamentals for NonEEs; © B. Rauf
Motor Power – Line Current Calculation:
Power rating, in HP (Horse Power) = P = 10 HP
Voltage Rating = 480 VAC
No. of Phases = 3; also stated as 3
Power Factor = PF = 0.8
Efficiency = Eff. = 0.9
Magnitude of Line Current = FLA, Full Load Current = I = I = ?
Note: 1 HP = 746 Watts = 746 W = 0.746 kW
Formula: I = Power in Watts / PF / Eff./ (3 x VL)
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Miscellaneous:
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Outputs From Simple Diode Circuits:
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Outputs From Simple Diode Circuits:
ElectronicsSpecial Types of Diodes:
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Bipolar Junction Transistors:
Bipolar Junction Transistor Operating Regions
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Power Distribution Systems Consist of:
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Bobby Rauf ©
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014
Power Factor, Definition, Concept and Formulas
Power Factor Correction / Improvement Example
Additional Comments / Discussion on Power Factor
Power Factor and Loss Calculation Example
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014
Power Factor, Definition, Concept and Formula:
Definition: Power Factor is defined as the Ratio of Real Power (kW) to Apparent Power (kVA). It is also defined as the quantity cos(  ).
PF = P/S or
PF = cos(  ),
where is the angle of voltage V, whereV = VRMS
is the angle of current i = I RMS
% PF = (PF) x 100
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014
Power Factor, contd.:
Leading Power Factor:
Power factor is said to be leading when, the angle of the current, exceeds , the angle of the voltage.
In other words, (  ) is negative.
Impedance, Zc, due to pure capacitance reactance, Xc, has a negative angle. Or, Zc = Xc 90
I
Zc= Xc 90=j Xc

V
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014
Power Factor, contd.:
Lagging Power Factor:
Power factor is said to be lagging when, the angle of the current, is less than , the angle of the voltage.
In other words, (  ) is positive.
Impedance, Zl, due to pure inductive reactance, Xl, has a positive angle. Or, Zl = Xl 90
In Inductive Circuits, add Capacitance, or Capacitive Reactance, Xc, to offset the Inductive Reactance, Xl, and to Increase the PF.
V
Zl= Xl +90=+j Xl
Pf Angle
= 
I
V
90 Deg.
I
V
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014
Power Factor, contd :
C = ( Q1  Q2 )
2 f V2
Where,
C = Capacitance (F) required to reduce the
Reactive or Imaginary Power from Q1 toQ2
Q1 = Initial, higher Reactive Power, in VARs
Q2 = Improved, lower Reactive Power, in VARs
V = Voltage, in Volts
f = Frequency, in Hz
Electrical Engineering Fundamentals for NonEE's; © B. Rauf
3/10/2014