6.7 Conduction, Reactive Power & Maximum Power Transfer

6.7 Conduction, Reactive Power & Maximum Power Transfer

Quick Answer: Halving cross-sectional area doubles resistance. Descending conductivity: silver, copper, aluminium, iron, lead. Reactive power shuttles between magnetic and electric fields and is not dissipated. True power = apparent power × power factor. Maximum power transfer happens when load impedance = source internal impedance.

Sub-topic 3-A-008 (Conduction) is broader than its title suggests. It bundles conductor geometry, the conductivity league table, the nature of reactive power, and the maximum power transfer theorem—four ideas that reappear throughout Element 3.

Conductor geometry and resistance

Halving the cross-sectional area of a conductor will double the resistance.

Resistance follows R = ρL / A, where ρ is resistivity, L is length, and A is cross-sectional area:

Area appears in the denominator, so resistance is inversely proportional to it—that is the whole trick. Note also that wire gauge numbering runs backwards: a larger AWG number means a thinner wire and therefore more resistance per foot. Going from AWG 14 to AWG 17 roughly halves the area and roughly doubles the resistance.

Recall from section 6.5 that at RF the skin effect confines current to the surface, so the DC cross-sectional area stops telling the whole story—an important caveat when you are sizing an RF ground strap rather than a DC feed.

The conductivity league table

Which group is correct for listing common materials in order of descending conductivity? Silver, copper, aluminium, iron, and lead.

Only the ordering matters for the exam. If an option opens with copper before silver, or places aluminium above copper, it is wrong.

Reactive power: energy that never leaves

What happens to reactive power in a circuit that has both inductors and capacitors? It alternates between magnetic and electric fields and is not dissipated.

This is the conceptual heart of AC power and worth getting genuinely right rather than memorising.

• An inductor stores energy in a magnetic field while current rises, then returns it to the circuit as current falls.
• A capacitor stores energy in an electric field while voltage rises, then returns it as voltage falls.
• Because their storage phases are opposite, in a circuit containing both, energy sloshes back and forth between the two fields.

None of that energy is converted to heat. Only resistance dissipates power. That is why an ideal inductor or capacitor consumes no real power no matter how large the circulating current—and also why a badly power-factor-corrected installation can circulate large currents (with real I²R losses in the wiring) while delivering little useful work.

True, apparent, and reactive power

How do you compute true power in a circuit where AC voltage and current are out of phase? Multiply apparent power times the power factor.

That relationship is asked in two sub-topics — here and in 3-B-013 — so it is worth two marks. The companion numbers from the electrical-math topic:

Those three middle values are asked directly. Note the pattern: cos 60° = 0.5, not 0.866. Candidates who memorise sines instead of cosines reverse 30° and 60°.

Maximum power transfer

Assuming a power source to have a fixed value of internal resistance, maximum power will be transferred to the load when the load impedance equals the internal impedance of the source.

The reasoning is a balance. If the load impedance is much lower than the source impedance, current is high but most of the voltage drops inside the source. If the load is much higher, the voltage divides favourably but almost no current flows. The product V × I in the load peaks exactly at the match point.

Two cautions that matter professionally:

1. Maximum power transfer is not maximum efficiency. At a perfect match, half the total power is dissipated inside the source, so efficiency is 50%. Power distribution systems deliberately run a very low source impedance into a much higher load for efficiency; RF systems match because getting the signal out matters more than heat in the final.
2. This theorem is why RF systems are built around a consistent characteristic impedance—50 ohms for most commercial radio work. Matching transmitter, feed line, and antenna is the practical application, and it drives the transformer turns-ratio and SWR material in sections 7.6 and 16.3.