E5: Electrical Principles
Subelement E5 covers the mathematical and physical foundations of AC circuits used throughout amateur radio engineering: resonance and the quality factor Q in series and parallel RLC circuits; RC and RL time constants and phase relationships including admittance and susceptance; rectangular and polar coordinate systems and phasor diagrams for representing complex impedance; and RF-specific effects in real components including skin effect, parasitic reactance, self-resonance, and the distinction between real and reactive power.
The Extra exam draws four questions from E5 — one from each group. These questions are quantitative and conceptual, requiring you to apply formulas, interpret phase relationships, work in both rectangular and polar notation, and understand how ideal circuit behavior breaks down at RF frequencies.
Study These Topics
E5A: Resonance and Q
Resonant frequency formula, series vs. parallel RLC behavior at resonance, impedance at resonance, circulating vs. input current, Q calculation for series and parallel circuits, half-power bandwidth, and the effect of Q on internal voltages and matching bandwidth.
Study E5AE5B: Time Constants and Phase
RC and RL time constants, the 63.2%/36.8% rule, phase angle calculation in series RLC circuits, voltage-current phase relationships in capacitors and inductors (ELI the ICE man), admittance, susceptance, and converting between impedance and admittance in polar form.
Study E5BE5C: Coordinate Systems and Phasors
Rectangular notation (R ± jX), polar notation (magnitude ∠ angle), plotting impedance on rectangular coordinates, pure resistance on the horizontal axis, capacitive reactance as negative j, inductive reactance as positive j, phasor diagrams, logarithmic frequency response axes, and impedance point identification on graphs.
Study E5CE5D: RF Effects
Skin effect and increasing resistance at RF, short lead lengths to minimize inductive reactance and phase shift, why electrolytic capacitors fail at RF, inductor self-resonance from inter-turn capacitance, parasitic reactance and self-resonance, skin effect loss in film capacitors, real vs. reactive power, electrical length vs. conductor diameter.
Study E5DE5A: Resonance and Q →
← E4: Amateur Radio Practices