FE Exam Review Electrical Circuits

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FE Exam ReviewElectrical Circuits

• LT Aaron Still
• P.E. in Electrical Engineering

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Exam Strategies

• http//www.ncees.org/exams/fundamentals/
• Only 4 minutes per problem.
• Dont dwell on a problem.
• If it looks like it may take gt 4 minutes, then
  there is probably a trick (e.g. short, open,
  extra info).
• Do the ones you know. Make an educated guess at
  the ones you dont know.
• Answers are typically in SI unit. Set your
  calculator to engineering notation.
• Pay attention to units (degrees vs. radians)
• On multiple answer problems, look for the unique
  set of answers.

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Exam Strategies

• Know your calculator. Start using your exam
  calculator now.
• The following are allowed for the FE exam
• Hewlett Packard HP 33s
• Hewlett Packard HP 9s
• Casio 115 MS and 115 MS Plus
• Texas Instruments TI 30X IIS and TI 30X IIB
• Texas Instruments TI 36X

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Important Concepts

• Voltage (V) electric potential
• V e?d Electric field, distance moved between 2
  points
• Current (A) flow or movement of charge
• I dQ / dt
• Resistance (O) opposition to flow of charge
• R ?L / A in a conductor
• Rseries R1 R2 . Rn
• Rparallel (1/R1 1/R2 1/Rn)-1

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Important Concepts

• Ohms Law V IR
• Joules Law P IV I2R V2/R
• Capacitance (F) ability to store electric
  charge
• C eA / d
• Cseries (1/C1 1/C2 1/Cn)-1
• Cparallel C1 C2 . Cn
• ic(t) C dvc(t) / dt
• W ½CV2

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Important Concepts

• Inductance (H) ability to store magnetic energy
• L N2 µA / l
• Lseries L1 L2 . Ln
• Lparallel (1/L1 1/L2 1/Ln)-1
• vL(t) L diL(t) / dt
• W ½LI2
• DC Transients
• T RC or T L / R
• v(t) VF (VI VF)e-t/T
• i(t) IF (II IF)e-t/T

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Important Concepts

• Circuit Analysis Know 1 or 2 well and use them
• By Inspection (i.e. 2? 2? 1?)
• KVL
• KCL
• Nodal Analysis (KCL for each node)
• Mesh Analysis
• Superposition (for multiple sources)
• Thevenin Circuits Max Power to load

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Important Concepts

• AC Circuits
• v(t) Vp sin(?t?) ? 2pf f 1/T
• Vrms (root mean square) Vp/v2
• Z V / I VVrms??v IIrms??i
• Zc 1/(j?C) ZL j?L
• P VrmsIrmscos(?v - ?i) PF cos(?v - ?i)
• Q VrmsIrmssin(?v - ?i)
• S P jQ S2 P2 Q2

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Important Concepts

• Three-phase power
• Wye-wye system
• Iphase Iline Vline (v3)Vphase Ineutral 0
• Delta-delta system
• Vphase Vline Iline (v3)Iphase
• Op-Amps
• I- I 0 V V-
• Vout -Vin(Rf/Rin) or Rf(Va/Ra Vb/Rb )

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Sample Problem

• What to consider
• Capacitors in series are mathematically like
  resistors in parallel
• 10 pF in series with 10 pF 5 pF
• 10 µF in series with 10 µF 5µF
• 5 pF in series with
• 5 µF 5pF

Answer A
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Sample Problem

• What to consider
• 16? resistor is in parallel with the 60V source
• When shorting the source for RTH, 16 ? is also
  shorted ?
• RTH 4 ? 12 ?
• V16? 60V ?
• V12? which is in series with 4 ?
• VTH 60V12? /(12? 4?) 45V

Answer A
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Sample Problem

• What to consider
• Magnitude of a phasor is always the RMS value
• Irms .7071 x Ipeak
• The peak for the current occurs after the peak of
  the voltage ? I lags V
• If Vphase 0?, then Iphase must be negative

Answer A
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Sample Problem

• What to consider
• Does the summing-point constraint apply? Yes
• I- I 0 A
• V- 0 V
• I1k? I10k? 2V/1k? ?Vo -(10k?)(I1k?)

Answer B
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Sample Problem

• What to consider
• Magnitude square root of the sum of the squares
  ?
• (32 42)0.5 5
• Phase angle inverse tangent of imaginary
  component over real component
• ? tan-1(4/3) gt 45?
• ? angle is positive because imaginary component
  is positive

Answer D
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Sample Problem

• What to consider
• Magnitudes multiple or divide
• Angles add or subtract
• Note if you calculate z1/z2, you get 1.49 so
  (b) is the answer with no further work

Answer B
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Sample Problem

• What to consider
• After t 5?, the capacitor acts like an open
  circuit ?
• the right 10V source and the 2? resistor are not
  factors to Vx
• Use Ohms Law for Ix
• Use voltage divider for Vx

Answer C
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Sample Problem

• What to consider
• Total power dissipated is due to the voltage,
  current, and resistance of the power line only.
• The power lines rating (10kV) and length(5 km)
  are extra info.
• Use Joules Law ?
• P I2R

Answer C
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Sample Problem

• What to consider
• With terminals shorted, the only resistance in
  the circuit is the internal resistance of the
  battery.
• Use Ohms Law ?
• R V / I

Answer A
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Sample Problem

• What to consider
• Recall it takes 5T for a capacitor to fully
  charge.
• T RC 15 ms ?
• 5T 75 ms
• Only 24 ms gt T so it must be the answer
• vc(t) Vf (Vi-Vf)e-t/T
• 1-e-5 0.993
• 1-e-x 0.8 ? x 1.6T

Answer D
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Sample Problem

• What to consider
• Inductances are mathematic like resistors in
  series and in parallel.
• Leq L1 L2
• IL 10 A from current source
• Energy stored in an inductor
• W(Joules) 0.5(LI2)
• Recall energy stored in a capacitor
• W(Joules) 0.5(CV2)

Answer B
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Sample Problem

• What to consider
• Iavg(AC) 0 so ignore the AC Source (short it)
• A fully-stored inductor has current but no
  voltage ? the 5? resistor is shorted out.
• Use Ohms Law
• I V/R 12V/10?

Answer C
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Sample Problem

• What to consider
• Find Req
• 2? 4? 4?
• Use Ohms Law
• I V/Req

Answer C
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Sample Problem

• What to consider
• Pavg I2rmsR
• I2R/2
• (20 A)2 50?/2
• 10000 W
• 10 kW

Answer B
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Sample Problem

• What to consider
• Iline Vline / (v3) Xline
• Xline v(30024002)
• In a balance wye-connected circuit,
• Iline Iphase
• In a balance threephase system, Ineutral 0

Answer B
Answer B
Answer A
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Sample Problem

• What to consider
• The input current into an op-amp is so small that
  it is negligible ? 0 A
• if v1/R1 v2/R2 0.875A
• vo - if Rf

Answer C
Answer A