Electrical Theory and Fundamentals
What this domain tests
The Electrical Theory and Fundamentals domain checks whether you can predict how a low-voltage circuit behaves before you install it. Expect Ohm’s law, power, series and parallel networks, AC impedance, conductor resistance, and voltage drop on long 24 V and 12 V runs.
Core relationships
- Ohm’s law: V = I × R. Power: P = V × I; in a resistor P = I²R = V²/R.
- Series: current is common; resistances add; voltages add.
- Parallel: voltage is common; conductances add, so RT = 1/(1/R1 + 1/R2 + …). Two equal resistors in parallel give half the resistance.
- AC circuits use impedance Z, not resistance alone. Apparent power is V × I in VA; real power is V × I × power factor in watts. A 24 VAC transformer rated 40 VA can supply 40 VA, not necessarily 40 W.
- Conductor resistance is published per 1,000 ft (NEC Chapter 9, Table 8) and rises with temperature. For a two-wire circuit, Vd = 2 × L × I × R_per_ft, where L is the one-way length.
Worked example
A 24 Vdc camera draws 0.5 A at the end of a 150 ft run of 18 AWG copper. Table 8 gives 6.51 Ω per 1,000 ft. The loop resistance is 2 × 150 ft × 6.51/1,000 = 1.953 Ω. Voltage drop is 0.5 A × 1.953 Ω = 0.98 V, or 4.1 percent. The camera sees about 23.0 V. If its datasheet lists 21.6 V minimum, the run is acceptable; if it lists 23.5 V minimum, move to 16 AWG or shorten the run.
Traps that cost marks
- Using the one-way length in the 2L formula. That halves the calculated drop and is the most common error.
- Mixing RMS and peak values. A “24 V” AC transformer is usually 24 V RMS; its peak is about 34 V.
- Adding parallel loads as if they were series. Four 8 Ω speakers in parallel are 2 Ω, not 32 Ω.
- Ignoring terminations, connectors, and temperature. A calculation that is barely inside the limit at 25 °C may fail at 60 °C.