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Electrical Engineering Essentials

A quick reference guide for fundamental concepts, formulas, and components in electrical engineering. This cheat sheet covers circuit analysis, electromagnetics, digital logic, and power systems.

Circuit Analysis Fundamentals

Basic Circuit Elements

Resistor (R)

Opposition to current flow. Measured in Ohms (Ω). Ohm’s Law: V = IR

Capacitor (C)

Stores electrical energy. Measured in Farads (F). I = C(dV/dt)

Inductor (L)

Stores energy in a magnetic field. Measured in Henries (H). V = L(dI/dt)

Voltage Source (V)

Provides a constant voltage. Ideal voltage source has zero internal resistance.

Current Source (I)

Provides a constant current. Ideal current source has infinite internal resistance.

Circuit Laws

Kirchhoff’s Current Law (KCL)

The algebraic sum of currents entering a node is zero. ∑ I = 0

Kirchhoff’s Voltage Law (KVL)

The algebraic sum of voltages around a closed loop is zero. ∑ V = 0

Ohm’s Law

Relates voltage, current, and resistance: V = IR

Power (P)

Rate at which energy is transferred. P = VI = I^2R = V^2/R

Series Resistors

Equivalent resistance: R_eq = R_1 + R_2 + ... + R_n

Parallel Resistors

Equivalent resistance: 1/R_eq = 1/R_1 + 1/R_2 + ... + 1/R_n

Circuit Analysis Techniques

Nodal Analysis: Solve for node voltages using KCL. Choose a reference node (ground).

Mesh Analysis: Solve for loop currents using KVL. Suitable for planar circuits.

Superposition Theorem: Find the response due to each independent source acting alone, then sum the individual responses. Only applicable for linear circuits.

Thevenin’s Theorem: Replace a complex circuit with a voltage source (V_th) in series with a resistor (R_th).

Norton’s Theorem: Replace a complex circuit with a current source (I_n) in parallel with a resistor (R_n). R_n = R_th

Electromagnetics

Fundamental Constants

Permittivity of Free Space (ε₀)

ε₀ ≈ 8.854 × 10⁻¹² F/m

Permeability of Free Space (μ₀)

μ₀ = 4π × 10⁻⁷ H/m

Speed of Light (c)

c ≈ 3 × 10⁸ m/s

Electrostatics

Electric Field (E)

Force per unit charge. E = F/q (N/C or V/m)

Electric Potential (V)

Potential energy per unit charge. V = U/q (Volts)

Coulomb’s Law

Force between two point charges: F = k * (q₁q₂) / r², where k = 1 / (4πε₀)

Capacitance (C)

Charge stored per unit voltage: C = Q/V (Farads)

Magnetostatics

Magnetic Field (B)

Measured in Tesla (T) or Webers per square meter (Wb/m²)

Magnetic Force (F)

On a moving charge: F = q(v x B)

Ampère’s Law

Relates magnetic field to current: ∮ B ⋅ dl = μ₀I_enc

Inductance (L)

Ability of a conductor to store energy in a magnetic field: L = Φ/I (Henries)

Electromagnetic Waves

Maxwell’s Equations (Differential Form):

∇ ⋅ D = ρ

∇ ⋅ B = 0

∇ × E = -∂B/∂t

∇ × H = J + ∂D/∂t

Poynting Vector (S): Represents the power flow of an electromagnetic wave. S = E x H (W/m²)

Wave Impedance (η): Ratio of electric field to magnetic field in a medium. η = √(μ/ε)

Digital Logic

Basic Logic Gates

AND Gate

Output is 1 only if all inputs are 1.

OR Gate

Output is 1 if at least one input is 1.

NOT Gate

Inverts the input. If input is 1, output is 0, and vice versa.

NAND Gate

NOT + AND. Output is 0 only if all inputs are 1.

NOR Gate

NOT + OR. Output is 1 only if all inputs are 0.

XOR Gate

Exclusive OR. Output is 1 if inputs are different.

Boolean Algebra

Basic Theorems:

A + 0 = A

A + 1 = 1

A ⋅ 0 = 0

A ⋅ 1 = A

A + A = A

A ⋅ A = A

Commutative Laws:

A + B = B + A

A ⋅ B = B ⋅ A

Associative Laws:

(A + B) + C = A + (B + C)

(A ⋅ B) ⋅ C = A ⋅ (B ⋅ C)

Distributive Laws:

A ⋅ (B + C) = A ⋅ B + A ⋅ C

A + (B ⋅ C) = (A + B) ⋅ (A + C)

DeMorgan’s Theorems:

(A + B)’ = A’ ⋅ B’

(A ⋅ B)’ = A’ + B’

Combinational Logic Circuits

Multiplexers (MUX): Select one of several input signals and forward it to the output.

Demultiplexers (DEMUX): Direct a single input signal to one of several outputs.

Encoders: Convert a set of inputs into a binary code.

Decoders: Convert a binary code into a set of outputs.

Adders: Perform binary addition (Half Adder, Full Adder).

Sequential Logic Circuits

Flip-Flops: Basic memory elements (SR, D, JK, T).

Registers: Groups of flip-flops used to store binary information.

Counters: Sequential circuits that count pulses (Asynchronous, Synchronous).

Power Systems

AC Power Fundamentals

RMS Voltage (Vrms)

Root Mean Square voltage. Vrms = Vpeak / √2 (for sinusoidal waveforms)

RMS Current (Irms)

Root Mean Square current. Irms = Ipeak / √2 (for sinusoidal waveforms)

Apparent Power (S)

S = VI* (VA)

Real Power (P)

P = VI cos(θ) (Watts)

Reactive Power (Q)

Q = VI sin(θ) (VARs)

Power Factor (PF)

PF = cos(θ) = P / |S|

Transformers

Turns Ratio (a): a = Np / Ns = Vp / Vs = Is / Ip
Np, Ns: Number of turns in primary and secondary windings.
Vp, Vs: Voltage in primary and secondary windings.
Ip, Is: Current in primary and secondary windings.

Ideal Transformer Equation: Vp * Ip = Vs * Is

Three-Phase Power

Line Voltage (V_L)

Voltage between two lines in a three-phase system.

Phase Voltage (V_ph)

Voltage across a single phase.

Line Current (I_L)

Current flowing through a line in a three-phase system.

Phase Current (I_ph)

Current flowing through a single phase.

Y-Connection

V_L = √3 * V_ph, I_L = I_ph

Delta-Connection

V_L = V_ph, I_L = √3 * I_ph

Three-Phase Power (P)

P = √3 * V_L * I_L * cos(θ)

Power System Protection

Fuses: Overcurrent protection. Melt and interrupt the circuit.

Circuit Breakers: Overcurrent protection. Can be reset after tripping.

Relays: Detect abnormal conditions and initiate protective actions.

Grounding: Provides a low-impedance path for fault currents.
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