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# EE PE Power Exam

### Flashcards for the Electrical Engineering Power PE Exam

What is the Motor Slip Equation? What is motor slip? %slip = (n[s]-n)/n[s]*100 ; (speeds are in RPMs - where n[s] = synchronous speed, n=motor or actual speed);
How does Horsepower relate to KW? Hp=KW*efficiency/746; OR 1 Hp=.746KW*efficiency; OR 1 KW = 1.34 hp/efficiency; OR .746 KW/Hp; OR 746 W = 1 Hp
What is synchronous speed? How is it measured? The synchronous speed (n[s]) of an AC induction motor is the theoretical speed at which the motor should spin if the induced magnetic field in the rotor perfectly followed the rotating magnetic field of the stator. Measured in RPMs.
What is a stator? The stationary member of an electrical machine, as of an induction motor.
What is the equation for RPM? What is the symbol and description of RPM? RPM = 120*f/(# Pole-pairs) (where f=frequency, usually 60 Hz); RPM is w (omega) - rotational speed.
How do you calculate efficiency? efficiency = P[out]/P[in]
What are the Voltage and Current line and phase relationships for a Wye configuration? For a Delta Configuration? Wye: Line Current = Phase Current; Line Voltage = Phase Voltage x sqrt(3); Delta: Line Current = Phase Current x sqrt(3)Line Voltage = Phase Voltage
What is the form of a complex number in rectangular form? How do you find the magnitude? Real + j*complex (ex. 1+j1); Magnitude: pythagorean - sqrt(1^2+1^2)=sqrt(2)
What is the form of a complex number in polar form? magnitude*angle - for 1+j1 -> sqrt(2)<45degrees
What is the form of a complex number using exponentials? magnitude*e^(j*angle) (angle in radians); for 1+j1 = sqrt(2)e^(j*pi/4)
What are two forms of Euler's equation? 1st: e^(j*theta)=cos(theta) + jsin(theta); 2nd: e^(j*theta)+e^-(j*theta)=2cos(theta)
Which complex methods should be used for which algebraic functions? (add, subtract, mult., div., powers) Addition - Rectangular; Subtraction - Rectangular; Multiplication - Polar or Complex Exponential; Division - Polar or Complex Exponential; Powers - Polar or Complex Exponential
Describe the roots and the waveform of the three possible root solutions (for b^2-4ac >,=,< 0) b^2-4ac>0, 2 complex conjugate roots (overdamped); b^2-4ac=0, 2 real, identical roots (critically damped); b^2-4ac<0, 2 complex conjugate roots (underdamped)
If you can't factor the denominator nicely, what method should you use to factor an expression? Method of Undetermined Coefficients
What is the Method of Undetermined Coefficients? For (x^2+3x+1)/(x^3+x^2+x)? For denominators that can't be factored nicely. (x^2+3x+1)/(x^3+x^2+x)=.../x(x^2+x+1)=C/x+(Ax+B)/(x^2+x+1)=(C(x^2+x+1)+(Ax+B)*x)/x(x^2+x+1) -> Multiply out and set coefficients of similar exponents equal to each other on each side of equation.
What are two equations for a straight line? y=mx+b; (y-y1)/(x-x1)=(y2-y1)/(x2-x1)=m
What is the form of a 1st order diff. eq.? What is its solution? Equation: b(dx/dt)+cx=d; Solution: x=d/c+Ae^(-ct/b)
What is the form for a 2nd order diff. eq.? Where in the book are the solutions found? a(d^x/dt^2)+bdx/dt+cx=d; Found on p.1-7, 1-8 (Eqns 1.72, 1.76, 1.80)
What is the average value of a waveform? It is DC (Direct Current); DC=1/T*int[0 to T](f(t)dt)
What are Laplace Transforms of 1, f(t), df(t)/dt, d^2f(t)/dt^2? L(1)=1/s; L[f(t)]=F(s); L[df(t)/dt]=sF(s)-f(0+); L[d^2f(t)/dt^2]=s^2F(s)-sf(0+)-df(0+)/dt; (f(0+) and df(0+)/dt is initial condition on real side)
What is the Initial Value Theorem? If X(s) exists in Laplace world, you can find X(0) in real world by mult by x(s)*s and taking limit as s approaches infinity and setting equal to x(0) in time domain.
For Laplace, what do you do for infinity/infinity? Multiply by s^2/s^2 (or basically, (1/s^2)/(1/s^2)) to get infinity's in denominators and creating zeros rather than infinity's.
What is the Final Value Theorem? What are the two hints to remember? Given X(s), Final Value is value of X(A) at infinity? To get it, multiply by s, then take limit as s -> 0.Hints: when t->0, lim(s)->infinity;When t->infinity, lim(s)->0
How do you convert angular frequency to frequency? To Period? w[o]=2*pi*f[o]=2*pi/T (T=period=1/f[o])
See Transfer Function/Fourier Transform example in notebook. Look for marked page.
Convert 1.78e^j1.879 to polar using calculator. Ans: 1.78<107.7degrees; To get: Type in full answer and convert using shift r<0 (or whatever you're looking for) - 1st term is given. Do "shift =" to get imag. part or angle part.
What does Nyquist sampling criterion say? You need to sample at least twice as fast as the fastest frequency in the system. (May not be enough samples in Discrete Fourier - called aliasing). Page 1-12.
How do you find the Laplace of a function that is a combination of two simple functions (like a ramp for five seconds and a plateau for the remaining time)? Combo of a ramp with a slope and a negative ramp after a delay of say, 10 seconds), for the remaining time. Add the 1st ramp to the 2nd with the 2nd having a 10 sec delay. Ramps in Laplace are slope/s^2. 10 sec. delay is e^-10s. Prob 1-27 soln. in notes.
How do you integrate in Laplace? How do you go from pulse to ramp? Just divide by s! To go from pulse to ramp, integrate.
What is the method of getting the transform of the output of a system? Transform of input X Transform of system = Transform of output
How do you find the resistivity at a given temperature? Res[t]=Res[20-degrees](1+alpha[20](T-20)); alpha[20-Cu]=3.9x10^-3 per degree; alpha[20-Nichrome]=17x10^-5 per degree; Res[20-Cu]=1.8x10^-8 ohm-m; Res[20-Nichrome]=1.08x10^-6 ohm-m
How do you find what the resistance of a conductor is? Resistance=Resistivity[T]*Length/Area (or R=Res[T]*L/A)
How do you find area of AWG#30? (P. 6-27 says AWG#30 is 100 circular mils.) Diameter^2=100 circ. mils; 1 mil = .001 inches; so Diameter is sqrt(100)=10 mils. 10 mils=.01 inches=2.54*10^-4 m; Area = Pi*d^2/4=5.07x10^-8 m^2.
How are capacitance, current, and voltage related? I=C*dv/dt
What is the equation for energy in a capacitor? W=1/2*CV[c]^2 ; (V[c]=Voltage across capacitor)
What is the voltage divider equation? V[R2]=(V[s]/(R1+R2)) * R2 ; (Because V[R2]=I[R2]*R2
What is the equation for voltage across an inductor? V[L]=L*dI/dt
What is the equation for energy in an inductor? W=1/2LI^2
How do you find the voltage in a transformer? V=N*dPhi/dt ; (N=# turns, Phi=flux) (Transformer taps use this b/c same flux throughout core, but if you tap off at different points, there are different turns prior to each tap, so voltage output is different at each tap.)
What do the polarity dots indicate in a transformer diagram? Positive Currents point into positive end of voltage. Or, When current enters the dot, the voltages are positive.
How are primary and secondary voltages in a transformer related? V1/N1=V2/N2=V3/N3
How are primary and secondary currents in a transformer related? N1I1+N2I2+N3I3=0 (At least one current is negative)
What is voltage regulation? Voltage Regulation = swing in output voltage between no load and full load. (V[nl]-V[fl])/V[fl] (Full load is aka rated voltage)
What is another name for Rated Voltage? Full Load Voltage
What are the three types of circuit parameters? Z - Impedence; Y - Admittance; H - Hybrid
What are the terms/variable symbols for the inverses of Impedence (Z), Resistance (R), Reactance (X)? 1/Z=Admittance (Y); 1/R=Conductance (G); 1/X = Susceptance (B),
What is the equation for the Hall Effect? What does the Hall Effect do? V[h]=IB[z]/nqw (B=magnetic flux, w=width, nq=total charge); The Hall Effect is the voltage drop from the top to the bottom of a conductor when that current-carrying conductor is placed in a magnetic field.
How does a 10V source in series with a 5 ohm resistor convert to a current source & resistor configuration? If this is in parallel with a 6V source (opposite polarity) and 10 ohm resistor, what is the equivalent voltage source configuration? 10/5=2A current source in parallel with 10 ohm (identical) resistor. 6/10=.6A in || with 10 ohm resistor. Current directions opposite, so subtract them (1.4A). Resistors in || = 3.33 ohms. 1.4(3.33)=4.67V in series w/ 3.33 ohms.
Convert (50mA current source || 1000 ohms) in series with (150mA current source [opposite polarity] || 400 ohms) to single current source. Parallels convert to series voltage sources and identical resistors -> Voltages subtract (b/c opposite polarity) -> Resistances add -> 10V/1400ohms = 7 mA || 1400 ohms.
Convert Voltage source with 30 ohm "T"ed with 60 ohm and 10 ohm with a load on the end to a Thevanin Equivalent Circuit. P. 2-17. 2/3V in series with 30 ohms
What are the two steps for finding the Thevanin Equivalent circuit? 1: W/ the terminals of the ckt open-ckt'd, determine the V across the terminals (V[th]); 2: With the term. short-ckt'd, determine the I[sc] (R[th]=V[th]/I[sc]). OR R[th]= Imped. looking into trmnls w/ all pwr srcs altr'd.
What is the Maximum Power Transfer Theorem (for R[2] on opposite side of transformer of R[1])? Max Pwr is Xferred from a fixed network to an imped. that is the cplx conj. of the Thev. Equiv. imped. of the fixed network. (note: when purely resistive, res. is the same as Xmission line load: R[2]=R[1]
If R[2] on right side of transformer is fixed and R[1] is variable, what gives maximum power transferred? Make R[1]=0 (not R[1]=R[2]) - Max Power Transfer Theorem for when line resistance is fixed!
For AC circuits, how do you find the maximum power transfer? The impedence that is the complex conjugate of the Thevanin Equivalent Impedence of the AC fixed network.
When you have a circuit bridge where two series resistors are in parallel with two other series resistors, and the voltage between the two parallel lines is zero, how do you find an unknown resistor in that system? Ratio on the left is the same as the ratio on the right. (1 ohm Series 2 ohm) || (10 ohm Series ? ohm) -> ? = 20 ohm IF V B/W IS ZERO!!!
In DC (Steady-State), what are R, L, and C? R stays the same; L is short-circuit (b/c @ DC, di/dt=0, so Volt. drop = 0 (L*di/dt=0); C -> dv/dt -> is an open-circuit
In AC (Steady-State), what are R, L, and C? R stays the same; L -> Z[L]=jwL; C -> Z[C]=1/jwC=-j/wC
In AC (Transient - not Steady State), what are Z[R], Z[L], and Z[C]? Z[R]=R; Z[L]=sL (using Laplace here -> s is like jw), Z[C]=1/sC
When working with RLC circuits using Laplace notation, what does "s" represent? When is this used? s=jw. This is used in transient (not steady-state) AC circuits.
How do you find the average of a waveform? (Area under a curve over a period)/period
How do you find the RMS? Do the opposite of Root-Mean-Square. In other words, Root of the Mean of the Square.
What does a voltmeter read? RMS Value of the Voltage.
Given a voltage function, how do you find the voltage spectrum? First convert voltage function to Power Spectrum (Eqns. 3.36-3.40), then convert that to voltage spectrum (Eqns. 3.41-3.44).
How is V[RMS] related to V[Peak]? V[RMS]=V[Peak]/sqrt(2)
In what form must angles be in to use exponential notation? Radians
Describe what it means vectorially when Current "lags" voltage. Is a lagging current capacitive or inductive? Angle between Voltage and Current is positive because, rotating clockwise, voltage is ahead of current. A lagging current is inductive. "ELI the ICE man" - Voltage Leads Current in Inductor...
How is the Power Factor found (2 methods)? P.F.=cos(theta) [or cos(theta-phi) if voltage and current both given a phase angle]. OR P.F.=P/S (b/c S*cos(theta)=P)
How is Power defined (equation) when using phasor notation? P=Re(VI*) (I* is complex conjugate [negative of the phasor angle]; Re is the real part [aka cosine]) - see page 3-16.
Draw the Power Triangle. Hypotenuse - S (in VA) is Apparent Power = i^2*Z; Theta is angle - P.F. = cos(theta); Opposite - Q (in VARs) is Reactive Power = i^2*X; Adjacent - P (in Watts) is Real Power = i^2*R
Give S equation in Rectangular Format. How do you calculate S given P and Q? S[rect] = P+jQ; Calculate S: S^2=P^2+Q^2 (Pythagorean)
How does the power triangle differ between capacitive and inductive circuits? If VARs are lagging, is that inductive or capacitive? Inductive has positive Q; Capacitive has negative Q. Lagging VARs = inductive.
Given a reactance (X), how can you tell if it is capacitive or inductive? Capacitive reactance is generally negative (to bring j [imaginary] to numerator from denominator).
What is sin(theta) in terms of P.F.? sin(theta)=sqrt(1-PF^2) (This assumes S has been normalized to 1.)
What is the Resolution of a 4-digit AC Digital Voltmeter? What is its Precision? Resolution is half of the least significant digit (4-digits' LSD is 1's place, so .5 is Resolution). Precision is Resolution/Largest Number (.5/9999)=.005%
How is Apparent Power defined using Phasor notation? S=VI* (I* is complex conjugate [negative phase angle of current]).
What is the Active Power absorbed by a motor? P=E[g]^2/R[core] + I[1]^2*R[1] {Stator Active Power} + I[1]^2R[2]/s {Active Power to rotor} Note: s=slip
What is the Reactive Power absorbed by a motor? Q=E[g]^2/X[m] + I[1]^2(X*phi[1]+x*phi[2])
What is the Apparent Power absorbed by a motor? VA=sqrt(P^2+Q^2)
What is the line current in a motor? What is another name for the line current in a motor? I[stator]=S/E[g]; Another name is Stator current.
What is the Active Power supplied to the Rotor? P[r]=I[1]^2*(R[2]/s) where s=slip. Note, this is the rotor portion of the active power absorbed by a motor.
What is the Power dissipated in the rotor conductors? P[LR]=I[1]^2*R[2]=sP[r]=s(I[1]^2*R[2]/s) where s=slip.
What is the Mechanical Power (P[m]) developed by a motor? P[m]=P[r](1-s) (derived in NPTel Video notes 4 pages before yellow paper clip).
What is the Torque developed by a motor? T=(P[r]/n[s])*(60/2Pi)
How is P[m] (Mechanical Power) related to P[r] (Rotor Power)? P[m]=(1-s)*P[r] (s=slip)
What does a RMS calibrated full-wave rectifier meter read? V[read]=Pi/(2*sqrt(2)) * V[avg]
What kind of meter gives this reading: V[read]=Pi/(2*sqrt(2)) * V[avg] RMS calibrated full-wave rectifier meter.
What does a D'Arsenval meter look for? Averages (or DC values)
What does an electrodynamometer read? True RMS (differs from other RMS b/c it removes any DC component and then measures the RMS)
A D'Arsenval meter reads 5 Volts. An RMS peak-to-peak meter reads 7 Volts. How do you find V[max] and V[min]? D'Arsenval -> V[avg]=(V[max]+V[min])/2=5; RMS-Peak-to-Peak -> V[read]=V[p-p]/2=V[peak] -> V[peak]/sqrt(2)=RMS voltage=7; Since V[p-p]=V[max]-V[min], V[rms]=V[max]-v[min]/(2*sqrt(2))=7; 2 Eqns, 2 Unknowns. P. 3-24, T-4.
What is the purpose of a 2-meter reading? One measures total power by getting the cosine value, while the other measures VARs (reactive power) by getting the sine value. Together, these can give all of power triangle information. P.3-25, T-6.
How does a DC voltmeter get its value? Net Area/Period=Avg
How does a RMS reading Full-Wave rectifier meter get its value? Pi/(2*sqrt(2))*V[Avg]
How does a RMS calibrated half-wave (diode) meter get its value? Pi/sqrt(2)*V[Avg]
How does a true RMS voltmeter get its value? What is a kind of true RMS voltmeter? sqrt[1/T*int{from 0 to T}((v(t)^2)dt)]. (Note: this is simply the root of the mean of the square). An electrodynamometer is a kind of true RMS voltmeter.
How does an RMS Peak Detector AC voltmeter get its value? V[peak]/sqrt(2)
How does an RMS Peak-to-Peak Detector AC voltmeter get its value? (V[max]-V[min])/(2*sqrt(2))
What is another term for Phase Voltage? For Line Voltage? V[phase]=Line-to-neutral Voltage; V[line]=Line-to-line Voltage
How is Line Current related to Phase Current in a Wye System? They are Equal.
How is Line Voltage related to Phase Voltage in a Wye System? V[line]=sqrt(3)V[phase]
How is Line Current related to Phase Current in a Delta System? I[line]=sqrt(3)I[phase]
How is Line Voltage related to Phase Voltage in a Delta System? They are Equal.
What is the symbolic terminology for Line Current? For Phase Current? Line Currents are I[a], I[b], I[c]; Phase Currents are I[ab], I[bc], I[ac].
How many voltages exist in a Wye System? How many currents? 6 Voltages in a Wye system; 3 or 4 Currents in a Wye system (depending on if the neutral is carrying current).
How many voltages exist in a Delta System? How many currents? 3 Voltages in a Delta system; 6 Currents in a Delta system.
In a Wye System, what is the vector value of V[ab]? Of V[bc]? Of V[ca]? V[ab]=sqrt(3)*|V[an]|*angle(30-degrees); V[bc]=sqrt(3)*|V[an]|*angle(-90-degrees); V[ca]=sqrt(3)*|V[an]|*angle(-210-degrees);
How do you find the phase angle (angle b/w line voltage and line current)? It is 30+theta (theta is impedance angle); Note: It is not just the impedance angle! Also note: phase angle depends on the nature of the impedance (capacitive, inductive, etc.)
In a Delta System, what is the vector value of I[a]? Of I[b]; Of I[c]? I[a]=sqrt(3)*|I[ab]|*angle(-30-degrees); I[b]=sqrt(3)*|I[ab]|*angle(-150-degrees); I[c]=sqrt(3)*|I[ab]|*angle(-270-degrees); (Note: Different than Wye Voltages)
Power factor is the angle between what? Phase Voltage and Phase Current (as opposed to the line quantities); Note: same for Wye and Delta.
How do you find the total power in a 3-phase system? P[total]=sqrt(3)*V[line]*I[line]*P.F.
What is Impedance in rectangular format? Z=R+jX
What are P, Q, and S in terms of Voltage and Current? P=VIcos(theta); Q=VIsin(theta); S=VI
What are the elements of the circuit equivalent of a transformer? R1=winding resistance primary; R2=winding resistance secondary; L1=Leakage inductance primary; L2=Leakage inductance secondary; G[c]=Core Conductance (or 1/R[c]); L[c]=Core Inductance; a=turns ratio
What is the Core Inductance? Flux needed to make transformer work - accounts for magnetization
What is the Core Conductance? Inverse of Core Resistance, which accounts for losses in the core.
How does R1 and R2 compare to R[core] in a transformer? R1 and R2 are small compared to R[core].
How does L1 and L2 compare to L[core] in a transformer? L1 and L2 are small compared to L[core].
How do you run an open-circuit test for a transformer? What assumptions can you make in this test? What information about the transformer does this test give? Open right-hand side of circuit (@ V2). Apply RATED voltage to left side and measure V[applied], I1 flowing into xfmr, and P in Watts measured during test. Assume R1 and L1 are negligible compared to R[c] and L[c]. Test tells us G[c] (or R[c]) and L[c].
How do you run an short-circuit test for a transformer? What assumptions can you make in this test? What information about the transformer does this test give? Short V[2] and apply SMALL voltage to left-hand side. Measure V1, I1, and P (Watts). Reflect R2 and L2 to primary. Assume R[c] and L[c] so big -> open circuit. This test gives us R1, L1, R2, and L2.
How do you reflect a resistance from the secondary to the primary? How about an inductance? R[p]=R[s]a^2; L[p]=L[s]a^2;
What current is applied for a short-circuit transformer test? RATED current is applied.
What are the 4 base quantities for the per-unit system? In 3-phase, what KVA, KV, or Current rating is used - total or per phase? KVA rating (S), KV rating (V), Current (I), Impedance (Z); KVA, KV, and I "per phase" ratings are used in 3-phase.
How do you find the base current? Base current = base kVA(1-ph)/base kV[phase]
How do you find the base impedance? Base impedance = base V[phase]/base current
How do you find the base kW[1-ph]? base kW[1-ph] = base kVA[1-ph] (note: same as kVAR[1-ph])
How do you find the base kVAR[1-ph]? base kVAR[1-ph] = base kVA[1-ph] (note: same as kW[1-ph])
What is the basic equation for finding the Per Unit values for Current, Voltage, Impedance, and Power? P.U.=Actual/Base (e.g. current P.U. = actual current/base current).
How are three-phase power systems usually specified? How would you get the base values needed from this? In terms of total KVA and line-to-line voltages. Base KVA is kVA[1-ph], so take the given (rated) kVA and divide by 3 (phases). Take the given V[line-to-line(line)] and divide by sqrt(3) for V[ln(phase)]. These are the bases needed for Per-Unit.
Learn Per Unit Well. Pages 5-8 to 5-10.
Given a primary and a secondary voltage, how do you find the turns ratio? a[ps]=V[p]/V[s]
How do you find the starting current for a motor? I[starting]=6*I[rated]*P.F.
When you hear "Fraction" or "Percent", what method should this trigger for solving the problem? USE P.U. when you hear "Fraction" or "Percent"!!!
Given rated Voltage and Rated KVA, how do you get base current? Rated values are base values, so simply divide rated KVA/rated Voltage to get base current.
How do you combine two transformers in series given their two sets of ABCD parameters? Matrix multiplication to get a single transformer set of ABCD parameters. [Top Row 1: A1 B1, Bottom Row 1: C1 D1]*[Top Row 2: A2 B2, Bottom Row 2: C2 D2]
If a motor is Wye-connected for starting, but delta-connected for running, how are the starting currents and impedances affected? What horsepower motor can be used? What if the motor was set up in Delta (starting) -> Wye? Wye -> Delta: I[Wye] = 3*I[Delta] (motor with 3X starting current, and thus 3X horsepower can be used); Z[Wye]=1/3*Z[Delta]; Conversely, switching from delta to wye results in 3x the starting Z and 1/3 starting current (1/3 Hp).
What is the skin effect? Electromagnetic phenomenon which determines the time needed for an external field to penetrate a conductor. This results in a higher current density near the surface than at the middle. Increase of resistance and decrease in internal inductance.
What is the skin effect equation (and the terms for the variables making it up)? delta=1/sqrt(Pi*f*mu/roe) ; f=frequency (Hz), mu=permeability (henrys/m), roe=resistivity (ohm-m)
How many inches is a mil? How do you convert meters to mils? A mil is .001 inches? mils = meters * 10^5/2.54.
Where is the mils conversion table in the book? P. 6-2, Table 6.1
What is the usual value for mu (permeability in conductance)? mu=4*Pi*10^-7 (for nonmagnetic materials).
What is the inductive correction factor for determining inductive reactance? K[L]=1+ln[D]/ln(1/GMR) (D and GMR in feet) (when spacing is other than 1 foot)
What are D and GMR (in determining inductive reactance)? Where do you find these values? D=center-to-center spacing of parallel wires; GMR = geometric mean radius (radius adjusted for the internal inductance of the conductor). Find these in Table 6.2.
What is GMR used for? GMR used ONLY for inductive reactance.
What is the correction factor for capacitance? How do you apply this? K[c]=1+ln(D)/ln(1/r); X[c]=X[c-table]*K[c]
How do you find the geometric mean of three-phase conductors? d[s]=cubedrt(r[ab]*r[bc]*r[ca]) (where r values of the distances between conductors)
How do you find the self-inductances for three-phase conductors? L=(2*10^-7)*ln(d[s]/GMR)
How do you find the Capacitive Reactance for three-phase conductors? X[c]=29,668*ln(d/r)ohm-miles (d=separation b/w each pair of conductors, r=radius of each of the three identical conductors). Actual capacitive reactance is obtained by multiplying by # of miles of conductor.
What are the distance ranges for short-range, medium-length, and long-distance transmission lines? Short: < 50 miles; Medium: 50 to 150 miles; Large: > 150 miles
For short transmission lines, what is V[r] and V[s]? How are they related? V[r]=receiving end voltage; V[s]=Sending end voltage. V[s]=V[r]+I[shunt]*z[line] (I[shunt]=I[s]=I[r])
For short transmission lines, what is V[r] at no-load? At no-load, V[r]=V[s] (b/c no current is flowing).
For short transmission lines at full-load, how do you find the voltage regulation? Voltage Regulation = |V[nl]-V[fl]|/|V[fl]|*100% (Note: V-full load in denominator, not no-load)
What is the main difference between evaluating short transmission and medium transmission? You can't neglect shunt capacitance in medium like you could in short.
If kW and kVA is given for a transmission line, how do you find the power factor? Do you assume lagging or leading? P.F. = kW/kVA ; assumed to be lagging
For long transmission lines, what is these partial derivatives? dV/dx, dI/dx, d^2V/dx^2, d^2I/dx^2? dV/dx=-Iz; dI/dx=-Vy; d^2V/dx^2=Vyz; d^2I/dx^2=Izy
For long transmission lines, what is y and z? y*dx is admittance for the section, z*dx is impedence for the section
For long transmission lines, how do you find the propogation constant (2 different answers)? gamma=sqrt(y*z); gamma=alpha+j*beta (so alpha+j*beta)=sqrt(y*z)
For long transmission lines, what is alpha and its units? alpha=attenuation constant; units: nepers per mile
For long transmission lines, what is beta and its units? Beta=phaseconstant; units: radians per mile
How do you find the voltage along a long transmission line? What do the different factors represent? V=[V1*e^(-alpha*x)e^(-j*beta*x)]+[V2*e^(alpha*x)e^(j*beta*x)] ; First term is voltage traveling left to right, second term is voltage traveling right to left.
How do you find the current along a long transmission line? What do the different factors represent? I = sqrt(y/z)*V1*e^(-alpha*x)*e^(-j*beta*x)-sqrt(y/z)*V2*e^(alpha*x)*e^(j*beta*x) ; First term is current waves traveling left to right, second term is current waves traveling right to left.
What is the variable for and how do you find the characteristic impedence of a long transmission line? z[o]=sqrt(z/y)
What are the ABCD parameters in long transmission lines? A=cosh(gamma*l) (l=length of line); B=z[o]sinh(gamma*l); C=1/z[o]*sinh(gamma*l); D=cosh(gamma*l)
What does VSWR stand for? What is it? Voltage Standing Wave Ratio. Ratio of the maximum RMS voltage along a transmission line to the minimum voltage.
How do you determine Z[max] and Z[min] in a transmission line? Z[max]=Z[o]*VSWR; Z[min]=Z[o]/VSWR
What is the equation for the input impedance? Z[i]=Z[o]*(Z[L]*cos(beta*l)+j*z[o]*sin(beta*l)/(z[o]*cos(beta*l)+j*Z[L]*sin(beta*l)) (where Z[L] is inductive impedance and l is length of line) Note: this is long but it was used quite a bit in examples, so it's worth learning.
Where in the book can you find the method for using the Smith chart? P. 6-15 - study this and learn how to use it. May need to bring a compass to use this chart - find out if a compass is allowed.
What can the Smith chart tell you? The input impedance seen by the generator.
When using the Smith chart, what r value should you use? Why? Use r-1 b/c this is normalized.
When dealing with transmission lines, what are mu and epsilon? How are they related in equation format? mu=permeability ; epsilon = permittivity; sqrt(u[o]/epsilon[o])=120*Pi OHMS
Given f (frequency), how do you find the phase constant? beta = omega/c = 2*Pi*f/c (c is speed of light)
In antennas, what is lamda? How do you find it? lamda is the wavelength of signal : lamda=c/f (c=speed of light)
In transmission lines, how do you find the half-wave dipole? h=lamda/4 (=(c/f)/4)
What is the Lorentz Force Equation? What is it used for? F=BIL (Force=Flux*Current*Length); When a wire carrying a current is placed in an electric field, it experiences this force. Another form is F=q(E + v X B) (all are vectors except q).