A 120-volt branch circuit protected at 20 amperes serves a steady 16-ampere load 75 feet from the panel. The conductors are 12 AWG solid uncoated copper, which Chapter 9, Table 8 lists at 1.93 ohms per 1,000 feet. Treating the circuit as a simple resistance and remembering that the current travels out and back, what is the approximate voltage drop?
- AAbout 2.3 volts
This uses the 75-foot one-way length. The current has to return on the second conductor, so the resistance in the loop is that of 150 feet of wire.
- About 4.6 volts
- CAbout 9.3 volts
This uses 300 feet, doubling the run and then doubling it again for the return path. The out-and-back doubling happens once.
- DAbout 5.8 volts
This uses the 20-ampere rating of the overcurrent device instead of the 16-ampere load. Drop depends on the current actually flowing, not on the size of the breaker protecting the circuit.
Why B is correct
Total conductor length is 75 feet out plus 75 feet back, or 150 feet. Resistance is 1.93 x (150 / 1,000) = 0.29 ohm. Ohm's law then gives 16 x 0.29 = 4.63 volts, about 3.9 percent of 120 volts. Working from table resistance is the same calculation as the constant method; only the way the conductor property is expressed changes.
What this question is testing
Tests whether you can build the total loop resistance from a per-1,000-foot figure and apply Ohm's law to it, and whether you use the actual load current rather than the overcurrent device rating when computing drop.
On the job
Manufacturers publish conductor resistance rather than a drop constant, and so does the Code's own conductor properties table, so this is the method you fall back on when a problem or a submittal hands you ohms per 1,000 feet. It also makes the physics visible: the circuit is nothing but a load in series with a length of wire, and the wire takes its share of the voltage in proportion to its resistance.
Memory technique
Out and back: the loop is always twice the run.
Exam tip
Ohms per 1,000 feet times the total feet of conductor in the loop, divided by 1,000, then multiply by the load current.
Where to look it up
Chapter 9, Table 8 lists dc resistance per 1,000 feet separately for solid and stranded, coated and uncoated conductors.