Electrical Engineering Essentials Cheatsheet

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.