Electrical Engineering Fundamentals: Circuits and Components

Fundamental Electrical Units

• Current: Ampere (A)
• Voltage: Volt (V)
• Resistance: Ohm (Ω)
• Power: Watt (W)
• Charge: Coulomb (C)

Metric Prefixes

• peta (P): 10^15
• tera (T): 10^12
• giga (G): 10^9
• mega (M): 10^6
• kilo (k): 10^3
• milli (m): 10^-3
• micro (µ): 10^-6
• nano (n): 10^-9
• pico (p): 10^-12
• femto (f): 10^-15

Significant Figures and Math

• Non-zero: Significant
• Leading zeros: Not significant
• Middle zeros: Significant
• Trailing decimals: Significant
• Addition/Subtraction: Match decimal places
• Multiplication/Division: Match significant figures

Core Electrical Concepts

When electrons move, they create current. Current is defined as I = Q/t, and voltage is V = W/Q.

Q represents coulombs (electrical charge). One volt is the potential difference between two points when one joule of energy is used to move one coulomb of charge. One ohm (1 Ω) is the resistance when one ampere (1 A) flows through a material under one volt (1 V) of potential.

Conductance (G) is the inverse of resistance (1/R). Resistor color codes: First two bands are digits, the third is the multiplier (number of zeros), and the fourth is tolerance.

Ohm's Law and Power

Ohm's Law: I = V/R. In a current-voltage graph, the slope represents conductance (G), where resistance is 1/G.

Energy (W) is the ability to do work, measured in joules. One joule is the work done when one newton of force is applied over one meter. Note: The symbol W for work should not be confused with the unit for power, the watt (W). There are 3.6 × 10^6 J in one kWh.

One Watt = one joule/second. Power formulas: P=IV, P=I^2R, and P=V^2/R. Always select a resistor with a higher power rating than required. Efficiency = (Pout / Pin) × 100%. Amp-hour (Ah) = I × t.

Series Circuits

Series circuits feature a single path for current. Core rules: Current is constant throughout; RT = R1 + R2 + R3 + ...; voltage splits across resistors.

• Voltage Sources: Add if in the same direction; subtract if reversed.
• KVL: VS = V1 + V2 + V3 + ...
• Voltage Divider: Vx = VS * (Rx / RT)
• Power: PT = P1 + P2 + P3 + ...

Parallel Circuits

Parallel circuits involve components connected between the same two nodes, creating multiple paths. Voltage is constant across all branches; current splits; RT is always smaller than the smallest resistor.

• Formulas: 1/RT = 1/R1 + 1/R2 + 1/R3 + ...
• Special Cases: RT = (R1 * R2) / (R1 + R2) or RT = R / n (for equal resistors).
• KCL: IT = I1 + I2 + I3 + ...
• Current Divider (2 resistors): I1 = IT * (R2 / (R1 + R2))

Combination Circuits

To solve combination circuits: Identify series and parallel sections, combine step-by-step to find RT, calculate total current, and work backward. Remember: Series circuits share current; parallel circuits share voltage.

Inductors

An inductor is a coil that stores energy in a magnetic field and opposes changes in current. The basic equation is v = L (di/dt), where L is measured in Henrys (H).

• Inductance Factors: L = (N^2 µ A) / l. More turns or a better core increases inductance.
• Lenz’s Law: Induced voltage opposes the change in current.
• DC Behavior: Acts as an open circuit at t=0 and a short circuit at steady state.
• Time Constant: τ = L / R. Steady state is reached after approximately 5τ.
• Energy Stored: W = (1/2) L I^2.
• AC Behavior: Inductive reactance XL = 2πfL. Voltage leads current by 90°.

Transformers

A transformer transfers electrical energy between two coils via a magnetic field. It functions only with AC.

• Turns Ratio: n = Nsec / Npri
• Voltage/Current Ratios: Vsec / Vpri = Nsec / Npri = Ipri / Isec
• Step-Up: Nsec > Npri (Voltage increases, current decreases).
• Step-Down: Nsec < Npri (Voltage decreases, current increases).
• Impedance Reflection: Zpri = (Npri / Nsec)^2 × Zsec