Electrical Theory, Circuits, and Calculations
What this domain covers
Electrical Theory, Circuits, and Calculations tests the math behind low-voltage power, control, and signal circuits: Ohm's law, power, series and parallel networks, voltage drop, AC impedance, and power-limited source calculations. Expect 12 VDC, 24 VDC, 24 VAC control, and PoE.
Core rules
- Ohm's law: V = I × R. Power: P = V × I = I²R = V²/R. Keep units consistent.
- Series: one current path, current is the same, voltages add, resistances add. Parallel: voltage is the same across branches, currents add, total resistance is less than the smallest branch.
- Kirchhoff's laws apply: current into a node equals current out; voltage around a closed loop sums to zero.
- Two-wire DC voltage drop: VD = 2 × K × I × L / CM, with K = 12.9 for copper and 21.2 for aluminum, L in feet, CM in circular mils. The factor 2 is the return conductor.
- NEC voltage-drop guidance is informational: about 3 percent on a branch and 5 percent total. Low-voltage devices often need tighter design to stay above minimum operating voltage.
- PoE budgets: 802.3af about 15.4 W at the PSE and 12.95 W at the PD; 802.3at about 30 W and 25.5 W; 802.3bt about 60/51 W or 90/71 W. Cable heating and bundle size matter.
Worked example
A 24 VDC camera draws 0.5 A at the end of a 150 ft one-way 18 AWG copper run. 18 AWG is about 1,620 circular mils. VD = 2 × 12.9 × 0.5 × 150 / 1,620 = 1.19 V, or about 5.0 percent of 24 V. The camera may still work, but it is at the practical limit. Moving to 16 AWG, about 2,580 circular mils, gives VD of about 0.75 V, or 3.1 percent, a safer design. The reasoning is to calculate the loop, not just the one-way length, and to compare the result to the device's minimum input voltage.
Traps that cost marks
Forgetting the return-path factor of 2; mixing peak and RMS values; using nominal voltage when the source is actually 13.8 V or 27 V; treating VA and W as identical on AC circuits with poor power factor; and adding parallel resistances by simple addition.