Principles and Practice of Engineering Exam (PE) Electrical and Computer Engineering (PE Electrical) Syllabus

Electrical and Computer Engineering (PE Electrical) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electrical and Computer Engineering (PE Electrical) in Principles and Practice of Engineering Exam (PE), not a summary of it.

1. 1

   Circuit Analysis and Fundamentals

   3 topics

   • DC and AC Circuits
     • Node and mesh analysis
     • Thevenin and Norton equivalents
     • Phasors and impedance
   • Power in AC Circuits
     • Real, reactive, and apparent power
     • Power factor and correction
     • Three-phase systems
   • Electromagnetics
     • Electric and magnetic fields
     • Inductance and capacitance
2. 2

   Power Systems

   4 topics

   • Generation and Transmission
     • Per-unit system
     • Transmission line models
     • Power flow concepts
   • Transformers and Machines
     • Single and three-phase transformers
     • Induction and synchronous machines
     • Motor starting and characteristics
   • Protection and Coordination
     • Fault analysis (symmetrical components)
     • Protective relays and fuses
     • Coordination studies
   • Codes and Safety
     • National Electrical Code applications
     • Grounding and bonding
     • Arc flash and NFPA 70E
3. 3

   Electronics, Signals, and Control

   3 topics

   • Electronic Devices
     • Diodes, transistors, and amplifiers
     • Operational amplifier circuits
     • Power electronics and converters
   • Signals and Systems
     • Time and frequency domain analysis
     • Fourier and Laplace transforms
     • Filters and frequency response
   • Control Systems
     • Transfer functions and block diagrams
     • Stability and root locus
     • Bode plots
4. 4

   Communications and Computer Systems

   3 topics

   • Communication Systems
     • Modulation techniques
     • Information theory and bandwidth
   • Digital Systems
     • Boolean algebra and logic design
     • Combinational and sequential circuits
   • Computer Architecture and Networks
     • Processors and memory
     • Network protocols and topologies

Electrical and Computer Engineering (PE Electrical) flashcards for Principles and Practice of Engineering Exam (PE)

22 of 51 cards from the Electrical and Computer Engineering (PE Electrical) deck — real questions with worked answers.

1. State Ohm's law relating voltage, current, and resistance, and give the formula for instantaneous power dissipated in a resistor.

   Ohm's law: $V = IR$. Power dissipated: $P = VI = I^{2}R = \dfrac{V^{2}}{R}$.

2. For a resistor $R$, inductor $L$, and capacitor $C$, what is the impedance of each in the phasor (frequency) domain?

   Resistor: $Z_R = R$. Inductor: $Z_L = j\omega L$. Capacitor: $Z_C = \dfrac{1}{j\omega C} = -\dfrac{j}{\omega C}$.

3. What is the resonant frequency of a series (or parallel) RLC circuit, in both rad/s and Hz?

   $\omega_0 = \dfrac{1}{\sqrt{LC}}$ rad/s, and $f_0 = \dfrac{1}{2\pi\sqrt{LC}}$ Hz, where the inductive and capacitive reactances cancel.

4. Define the time constant of an RC circuit and an RL circuit, and how long until the transient is essentially complete.

   RC: $\tau = RC$. RL: $\tau = \dfrac{L}{R}$. The transient is about 99% complete after $5\tau$.

5. Write the capacitor and inductor element laws relating current and voltage.

   Capacitor: $i = C\dfrac{dv}{dt}$. Inductor: $v = L\dfrac{di}{dt}$. Energy stored: $\tfrac{1}{2}Cv^{2}$ and $\tfrac{1}{2}Li^{2}$.

6. What is the RMS value of a sinusoid with peak amplitude $V_m$, and why is RMS used for AC power?

   $V_{rms} = \dfrac{V_m}{\sqrt{2}}$. RMS is the DC-equivalent value that delivers the same average power to a resistor.

7. Define real, reactive, and apparent power, and write the complex power expression.

   Real $P = VI\cos\theta$ (W), reactive $Q = VI\sin\theta$ (VAR), apparent $S = VI$ (VA). Complex power: $S = P + jQ = V_{rms} I_{rms}^{*}$.

8. Define power factor and distinguish leading from lagging power factor.

   $\text{pf} = \cos\theta = \dfrac{P}{S}$. Lagging pf: current lags voltage (inductive load). Leading pf: current leads voltage (capacitive load).

9. How do you size a shunt capacitor bank to correct power factor from $\theta_1$ to $\theta_2$ for a real power $P$?

   $Q_C = P\left(\tan\theta_1 - \tan\theta_2\right)$, where $\theta_1$ is the original and $\theta_2$ the desired (improved) power-factor angle.

10. In a balanced three-phase wye system, relate line-to-line voltage to phase voltage and line current to phase current.

    Wye: $V_{LL} = \sqrt{3}\,V_{ph}$ and $I_L = I_{ph}$. (In delta: $V_{LL} = V_{ph}$ and $I_L = \sqrt{3}\,I_{ph}$.)

11. Write the total real power for a balanced three-phase load in terms of line quantities.

    $P_{3\phi} = \sqrt{3}\,V_{LL} I_L \cos\theta$, with corresponding $Q = \sqrt{3}\,V_{LL} I_L \sin\theta$ and $S = \sqrt{3}\,V_{LL} I_L$.

12. State Gauss's law and Ampere's law in integral form (Maxwell's equations).

    Gauss: $\oint \vec{E}\cdot d\vec{A} = \dfrac{Q_{enc}}{\varepsilon_0}$. Ampere (with Maxwell term): $\oint \vec{B}\cdot d\vec{l} = \mu_0\left(I_{enc} + \varepsilon_0\dfrac{d\Phi_E}{dt}\right)$.

13. State Faraday's law of electromagnetic induction.

    $\varepsilon = -\dfrac{d\Phi_B}{dt}$; the induced EMF equals the negative rate of change of magnetic flux. The minus sign (Lenz's law) opposes the change.

14. Write the Lorentz force law for a charge $q$ moving with velocity $\vec{v}$.

    $\vec{F} = q\left(\vec{E} + \vec{v}\times\vec{B}\right)$, combining electric and magnetic forces on the charge.

15. Give the magnetic flux density inside a long solenoid and the speed of light in terms of $\mu_0$ and $\varepsilon_0$.

    Solenoid: $B = \mu_0 n I$ (n = turns per unit length). Speed of light: $c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}} \approx 3\times10^{8}\ \text{m/s}$.

16. Define magnetomotive force (MMF) and magnetic reluctance, and give the magnetic Ohm's law analogy.

    MMF: $\mathcal{F} = NI$. Reluctance: $\mathcal{R} = \dfrac{l}{\mu A}$. Magnetic circuit: $\mathcal{F} = \Phi\,\mathcal{R}$ (flux $\Phi$ analogous to current).

17. In power transmission, why is high voltage used, and how do line losses scale with voltage for a fixed power?

    Higher voltage means lower current for the same power, and $I^{2}R$ losses fall. For fixed $P$, $I \propto 1/V$, so line losses scale as $\propto 1/V^{2}$.

18. Define the per-unit system and write the formula for per-unit impedance.

    Per-unit normalizes quantities to chosen bases: $\text{p.u.} = \dfrac{\text{actual value}}{\text{base value}}$. Base impedance: $Z_{base} = \dfrac{V_{base}^{2}}{S_{base}}$, so $Z_{pu} = \dfrac{Z_{actual}}{Z_{base}}$.

19. How is per-unit impedance converted from an old base to a new base?

    $Z_{pu,new} = Z_{pu,old}\left(\dfrac{V_{base,old}}{V_{base,new}}\right)^{2}\left(\dfrac{S_{base,new}}{S_{base,old}}\right)$.

20. Compare the three transmission-line length models (short, medium, long) by what circuit elements they include.

    Short (<80 km): series $R+jX$ only. Medium (80-250 km): series impedance + lumped shunt admittance (nominal-$\pi$ or T). Long (>250 km): distributed parameters using hyperbolic functions.

21. Define voltage regulation of a transmission line or transformer.

    $\text{VR}\% = \dfrac{|V_{NL}| - |V_{FL}|}{|V_{FL}|}\times 100\%$, the rise in receiving-end voltage from full load to no load.

22. For an ideal transformer with turns ratio $a = N_1/N_2$, relate voltages, currents, and reflected impedance.

    $\dfrac{V_1}{V_2} = a$, $\dfrac{I_1}{I_2} = \dfrac{1}{a}$, and impedance referred to primary $Z_1 = a^{2} Z_2$.

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