Conductors and voltage drop

Conductors are the electrician's main material. Choosing the right size is a balance: too small and the wire overheats or delivers too little voltage to the load; too large and the job costs more than it should and the wire will not fit in boxes, conduit or terminals. This chapter explains what decides a conductor's resistance, how conductor sizes are numbered, how to calculate voltage drop on a branch circuit or feeder, and how to choose a conductor that keeps voltage drop within the code limits. Ampacity, the current a conductor can carry without overheating, is set by the code tables you will study in ELEC-120; voltage drop is the second check every electrician makes.

What decides a conductor's resistance

The resistance of a conductor depends on its material, length, cross-sectional area and temperature (Lesson 4 introduces resistivity in detail):

Here \(\rho\) is the resistivity of the material, \(L\) the length and \(A\) the cross-sectional area. In US practice, area is measured in circular mils (cmil) and resistivity is written as \(K\), in ohm-circular mils per foot: about 10.4 for copper at 20 °C (about 12.9 at 75 °C, the value the NEC voltage drop method commonly uses) and about 17 for aluminum at 20 °C. Then \(R = K\,L/\text{cmil}\), with \(L\) in feet.

• Longer conductors have proportionally more resistance.
• Larger conductors (more area) have proportionally less.
• Aluminum has about 1.64 times the resistivity of copper, so an aluminum conductor needs roughly two sizes larger to match copper.
• Resistance rises about 0.39% per °C for copper (Lesson 3). Conductors run warm under load, so calculations usually use resistance at the conductor's operating temperature, often 75 °C.

Conductor sizes

In North America, building wire up to size 4/0 is numbered in the American Wire Gauge (AWG) system. The numbering runs backwards: a smaller number means a larger wire. Every 3 gauge numbers the area doubles (and the resistance halves); every 6 gauge numbers the diameter doubles. Sizes larger than 4/0 are given by area in thousands of circular mils (kcmil): 250 kcmil, 500 kcmil and so on. A circular mil is the area of a circle 1 mil (0.001 in) across; a conductor's area in circular mils is its diameter in mils squared.

Approximate DC resistance of solid copper conductors (NEC Chapter 9, Table 8 gives exact values, including stranded conductors):

• 14 AWG: 2.525 Ω per 1000 ft at 20 °C; 3.07 Ω per 1000 ft at 75 °C.
• 12 AWG: 1.588 Ω per 1000 ft at 20 °C; 1.93 Ω per 1000 ft at 75 °C.
• 10 AWG: 0.999 Ω per 1000 ft at 20 °C; 1.22 Ω per 1000 ft at 75 °C.
• 8 AWG: 0.628 Ω per 1000 ft at 20 °C; 0.764 Ω per 1000 ft at 75 °C.
• 6 AWG: 0.395 Ω per 1000 ft at 20 °C; 0.480 Ω per 1000 ft at 75 °C.

Ampacity and voltage drop are separate checks. For small copper branch-circuit conductors, both the Canadian and US codes limit overcurrent protection to 15 A for 14 AWG, 20 A for 12 AWG and 30 A for 10 AWG in most applications, but a long run may need a larger conductor than the breaker size requires, purely to limit voltage drop.

Voltage drop

Because conductors have resistance, current through them causes a voltage drop (\(V = IR\)), so the voltage reaching the load is less than the voltage at the panel. On a two-wire circuit (single-phase, or DC), current flows out on one conductor and back on the other, so the loop length is twice the one-way distance:

where \(L\) is the one-way length and \(R\) the resistance per unit length of one conductor at operating temperature. Percentage voltage drop is \(V_d\) divided by the nominal voltage. Three-phase circuits use \(\sqrt{3}\) in place of 2 (ELEC-210).

The NEC does not make voltage drop a general requirement for branch circuits and feeders, but its informational notes recommend sizing conductors so that voltage drop is no more than 3% on a branch circuit or feeder and 5% in total from the service to the farthest outlet. Many specifications, energy codes and manufacturers' installation instructions make those limits binding, and some specific NEC articles (for example, for fire pumps and some sensitive equipment) do set enforceable limits.

How far can a circuit run?

Rearranging the formula gives the longest one-way distance for a given current and allowed drop:

Why voltage drop matters

Low voltage at the load causes real problems:

• Resistive loads deliver less: a 1500 W heater receiving 114 V instead of 120 V produces \((114/120)^2 = 90\%\) of its rating, about 1350 W.
• Motors draw more current at low voltage to produce the same mechanical power, so they run hotter, start sluggishly and fail sooner.
• Electronic equipment may reset or malfunction; LED drivers and controls may flicker.
• The lost voltage is wasted energy: the conductors turn \(I^2R\) into heat, all day, for the life of the installation.

Voltage drop measurements are also a powerful troubleshooting tool. A large drop across a short section of conductor or a single connection, measured under load, points to a loose or corroded termination, a common cause of overheating and fires. Thermal imaging cameras find the same faults by their heat.

Aluminum conductors

Aluminum is lighter and cheaper than copper and is widely used for services, feeders and utility lines. Because its resistivity is about 1.64 times copper's, an aluminum conductor is typically two AWG sizes larger than copper for the same job. Aluminum also needs care at terminations: it oxidizes, expands and contracts more than copper, and creeps under pressure, so it must be connected only to devices and connectors marked for aluminum (such as AL/CU), with the correct torque and, where required, an anti-oxidant compound. Small-gauge aluminum branch-circuit wiring installed in some homes in the 1960s and 1970s caused many overheated connections because of these issues.