G5: Electrical Principles – Ham Radio General License Study Guide

G5 covers the fundamental electrical theory that underpins how RF circuits behave: the opposition to AC current called reactance, how inductors and capacitors combine with resistance to form impedance, how resonance occurs and what it means for a circuit, how power and voltage are measured on a decibel scale, and how components behave when wired together in series or parallel. Three exam questions come from this subelement, one from each group.

G5A addresses reactance, inductance, capacitance, impedance, and resonance: the definition of reactance and how inductive reactance increases with frequency while capacitive reactance decreases, what impedance and admittance are, how resonance cancels reactance in an LC circuit, what letter symbols are used, and how transformers and transmission lines achieve impedance matching. G5B covers the decibel, power calculations, and sine wave measurements: how a 3 dB change relates to a factor of two in power, how to calculate power from voltage and resistance, how to find RMS voltage from peak values, what peak-to-peak voltage is from an RMS value, and how to determine PEP from peak-to-peak voltage across a load. G5C examines resistors, capacitors, and inductors in series and parallel combinations, plus transformers: how parallel resistors combine (reciprocal formula), how series inductors add directly, how parallel capacitors add, how series capacitors and parallel inductors use the reciprocal formula, how transformer turns ratios step voltage up or down, why the primary winding is heavier gauge in a step-up transformer, and how to calculate turns ratios for impedance matching.

G5A: Reactance and Impedance

Reactance is the opposition to the flow of alternating current caused by capacitance or inductance — it is measured in ohms and represented by the letter X. Unlike resistance, reactance depends on frequency. In an inductor, reactance increases as frequency rises. In a capacitor, reactance decreases as frequency rises. The two types therefore behave in opposite ways with changing frequency.

Impedance is the total opposition to AC current flow, combining both resistance and reactance, and is represented by the letter Z. It is defined as the ratio of voltage to current. Admittance — represented by Y — is the inverse of impedance, just as conductance is the inverse of resistance.

When inductive and capacitive reactances are equal in a series LC circuit, resonance occurs. At resonance, the two reactances cancel each other out, leaving only resistance — so the impedance of a series LC circuit is at its minimum at resonance. Impedance matching at radio frequencies can be accomplished with a transformer, a pi-network, or a length of transmission line — all three methods are valid.

G5B: Decibels and Power

The decibel (dB) is a logarithmic unit that describes power ratios. A 3 dB change represents a factor of approximately two in power — 3 dB more means twice the power, 3 dB less means half the power. A 1 dB loss corresponds to approximately a 20.6% reduction in power. The PEP-to-average power ratio for an unmodulated carrier is exactly 1.00 — the peak and average are identical for a continuous, unvarying signal.

Power calculations use three forms of Ohm's law: P = IV (power = current × voltage), P = V²/R (power = voltage squared ÷ resistance), and P = I²R (power = current squared × resistance). For AC sine waves, the RMS (root-mean-square) value is what produces the same power dissipation as an equivalent DC voltage. The RMS value of a sine wave equals the peak value divided by √2 (approximately 0.707), and the peak-to-peak value equals the peak value multiplied by 2. To find PEP from a peak-to-peak voltage across a load, first find the peak voltage (Vpp ÷ 2), then the RMS voltage (Vpeak ÷ √2), then P = Vrms² ÷ R.

In a circuit of parallel resistors, the total current equals the sum of the currents through each branch.

G5C: Series and Parallel Circuits

Resistors in parallel combine using the reciprocal formula: 1/Rt = 1/R1 + 1/R2 + ... The total resistance of parallel resistors is always less than the smallest individual resistor. Capacitors in parallel add directly (total capacitance increases), while capacitors in series use the reciprocal formula (total capacitance decreases). Inductors in series add directly (total inductance increases), while inductors in parallel use the reciprocal formula (total inductance decreases). To increase capacitance, add a capacitor in parallel. To increase inductance, add an inductor in series.

Transformers use mutual inductance to transfer energy between primary and secondary windings. The voltage ratio equals the turns ratio: V2/V1 = N2/N1. A step-up transformer increases voltage and decreases current; because the primary carries higher current, the primary winding wire is larger in diameter than the secondary. A 4:1 voltage step-down transformer connected with the signal applied to the secondary instead of the primary acts as a 4:1 step-up transformer, multiplying the input voltage by 4. For impedance matching, the turns ratio equals the square root of the impedance ratio: N1/N2 = √(Z1/Z2).

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