Electrical Engineering Board Exam Study Notes
Complete Reviewer for the Registered Electrical Engineer (REE) Licensure Examination
In This Guide
About the EE Board Exam
The Registered Electrical Engineer (REE) Licensure Examination is administered by the Professional Regulation Commission (PRC). It assesses competency in electrical engineering fundamentals and their practical applications.
Exam Subjects
- • Mathematics
- • Engineering Sciences & Allied Subjects
- • Electrical Engineering
Requirements
- • BS Electrical Engineering degree
- • Passing score: 70%
- • No subject below 50%
Part 1: Circuit Analysis
Basic Laws
Ohm's Law & Power
V = IR (Voltage = Current × Resistance)
P = VI = I²R = V²/R
Energy = Pt (Power × time)
Units
- Voltage: Volt (V)
- Current: Ampere (A)
- Resistance: Ohm (Ω)
- Power: Watt (W)
Kirchhoff's Laws
KCL (Current Law)
Sum of currents entering a node = Sum of currents leaving
ΣI_in = ΣI_out
KVL (Voltage Law)
Sum of voltage drops around a closed loop = 0
ΣV = 0
Series & Parallel Circuits
Series
- R_T = R₁ + R₂ + R₃...
- I_T = I₁ = I₂ = I₃...
- V_T = V₁ + V₂ + V₃...
Parallel
- 1/R_T = 1/R₁ + 1/R₂ + 1/R₃...
- I_T = I₁ + I₂ + I₃...
- V_T = V₁ = V₂ = V₃...
AC Circuit Analysis
AC Fundamentals
- v(t) = V_m sin(ωt + φ)
- Angular Frequency: ω = 2πf (rad/s)
- Period: T = 1/f (seconds)
- RMS Value: V_rms = V_m/√2 = 0.707 V_m
- Average Value: V_avg = (2/π) V_m = 0.637 V_m
Impedance
Resistor
Z = R
Phase: 0°
Inductor
Z = jωL = jX_L
V leads I by 90°
Capacitor
Z = 1/jωC = -jX_C
I leads V by 90°
Total Impedance: Z = R + jX = |Z|∠θ
|Z| = √(R² + X²), θ = tan⁻¹(X/R)
Power in AC Circuits
Real Power (P)
P = VI cos θ
Unit: Watt (W)
Reactive Power (Q)
Q = VI sin θ
Unit: VAR
Apparent Power (S)
S = VI
Unit: VA
Power Factor: pf = cos θ = P/S = R/|Z|
S² = P² + Q²
Part 2: Electrical Machines
Transformers
Transformer Equations
- Turns Ratio: a = N₁/N₂ = V₁/V₂ = I₂/I₁
- Ideal Transformer: V₁I₁ = V₂I₂ (Power in = Power out)
- Efficiency: η = Output Power / Input Power × 100%
- Voltage Regulation: VR = (V_NL - V_FL)/V_FL × 100%
Transformer Losses
- Core/Iron Losses: Hysteresis + Eddy current (constant)
- Copper Losses: I²R losses (varies with load)
- Maximum Efficiency: When copper loss = iron loss
DC Machines
DC Motor Types
Shunt Motor
- • Field winding parallel with armature
- • Constant speed characteristics
- • Good speed regulation
Series Motor
- • Field winding in series with armature
- • High starting torque
- • Never run without load (runaway)
DC Motor Equations
- E_b = V - I_a R_a (back EMF)
- E_b = (PφZN)/(60A) (generated EMF)
- T = (PφZI_a)/(2πA) (torque)
- P = E_b × I_a (mechanical power)
AC Machines
Synchronous Machines
- Synchronous Speed: N_s = 120f/P (rpm)
- Generator: Prime mover drives, produces AC
- Motor: Runs at synchronous speed only
- Power Factor Correction: Overexcited = Leading PF
Induction Motors
- Slip: s = (N_s - N_r)/N_s × 100%
- Rotor Speed: N_r = N_s(1 - s)
- Rotor Frequency: f_r = sf
- Torque ∝ sV² (at low slip)
- Starting Methods: DOL, Star-Delta, Autotransformer, VFD
Part 3: Power Systems
Three-Phase Systems
Wye (Y) Connection
- V_L = √3 × V_P
- I_L = I_P
- P = √3 × V_L × I_L × cos θ
Delta (Δ) Connection
- V_L = V_P
- I_L = √3 × I_P
- P = √3 × V_L × I_L × cos θ
Transmission Lines
Line Parameters
- Resistance (R): R = ρL/A (ohms)
- Inductance (L): L = 2 × 10⁻⁷ ln(GMD/GMR) H/m
- Capacitance (C): C = 2πε₀/ln(GMD/r) F/m
- ABCD Parameters: V_S = AV_R + BI_R, I_S = CV_R + DI_R
Protection Systems
Protective Devices
- • Circuit Breakers (ACB, VCB, OCB, SF6)
- • Fuses
- • Relays (overcurrent, differential, distance)
- • Lightning Arresters
Fault Analysis
- • Symmetrical (3-phase)
- • Unsymmetrical (L-G, L-L, L-L-G)
- • Sequence components (positive, negative, zero)
Part 4: Electronics
Semiconductor Devices
Diodes
- • Forward bias: Current flows
- • Reverse bias: No current (until breakdown)
- • Silicon V_f ≈ 0.7V
- • Rectifier, Zener, LED, Photodiode
Transistors
- • BJT: I_C = βI_B
- • MOSFET: Voltage controlled
- • Amplifier configurations: CE, CB, CC
- • Common Emitter: High gain
Op-Amps
Basic Configurations
Inverting Amplifier
A_v = -R_f/R_in
Non-inverting Amplifier
A_v = 1 + R_f/R_in
Summing Amplifier
V_out = -R_f(V₁/R₁ + V₂/R₂)
Difference Amplifier
V_out = (R_f/R)(V₂ - V₁)
Part 5: Philippine Electrical Code (PEC)
Wiring Methods
- Minimum wire size: 3.5 mm² for branch circuits
- Conductor ampacity: Based on insulation type and ambient temp
- Voltage drop: Max 3% for branch, 5% total (branch + feeder)
- Conduit fill: Max 40% for 3+ conductors
Grounding
- Equipment grounding: Required for safety
- Ground electrode: Rod, plate, concrete-encased
- Ground resistance: Max 25 ohms (single electrode)
- GEC sizing: Based on largest service conductor
Overcurrent Protection
- General loads: 125% of continuous + 100% non-continuous
- Motor circuits: 125% FLC for wire sizing
- Motor protection: 250% FLC max for inverse-time breaker
- Transformer protection: Primary ≤ 125% FLC
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