Voltage Drop

Short Definition 
Lower voltage at the electrical load than power source, due to resistance in the wire. 
For best performance, at 5 amps a voltage drop of no more than 5% is best. The maximum acceptable loss is 10% (at 5A).
Most charts for bus wiring use these rules to determine the length and gauge of wire.
Contents
Concept
Voltage Drop occurs when current flows through a conductor. It obeys Ohm's Law, where the amount of voltage drop is equal to the resistance times the current.
A wire has a certain amount of resistance, which in short runs in negligible. Over long distances it becomes an issue. Resistance is typically expressed in 'ohms per thousand feet' or some other similar measure. The resistance is a function of both the diameter and length of the wire. Light gauge wires such as 22 ga. are more resistive than heavy wire such as 14 ga typically used in house wiring.
For example, in house wiring, 14 ga is used for 15A circuits, but for 20A circuits 12 ga is specified. This is to minimize the voltage drop, and the I2R (I squared R) losses. Which appear as heat. Too much current, too much heat, means potential for a fire. (Note: these are for copper. Aluminum wire is even heavier for the same current capacity, sometimes called ampacity.)
Electrical codes specify the maximum voltage drop allowable, usually no more than 3%. If the voltage drop exceeds the specifications, changes are required. Load calculations are made prior to wiring to ensure everything meets Code. Even though the circuit is rated for 15A, codes usually only allow a maximum of 80% of the rated current, limiting the circuit to a maximum of 12A on a 15A circuit. If the load exceeds the maximum allowable current rating, an extra circuit must be installed.
For Digital Command Control this comes into play. DCC wiring must be more robust than the older Direct Current Block wiring, as one booster may supply the entire layout. Thus, the bus wires must be heavy gauge. This is done to reduce the voltage losses, which in turn mean more current is drawn to do the same work, which can result in a fried decoder. A drop of one volt between the booster and locomotive can cause problems. As stated above, a voltage drop of 5% is acceptable, and at 5A, a maximum voltage drop of 10%.
Practice
DCC typically uses two heavy gauge bus wires to distribute power to the track. At intervals, a wire is connected between the bus and the track, typically every three to six feet in HO. Since the de facto standard today is Nickel Silver rail, which has a higher resistance, the effect is to parallel a low resistance copper bus with the higher resistance rail. Ohm's law states that the sum of resistors in parallel is less than that of the lowest resistor. Which means that the bus wire effectively negates any resistance in the rail. Current travels mostly in the lower resistance bus wire along the track instead of relying on the track to carry all the current. Which reduces the voltage drop.
A good example of voltage drop in action is a car battery. It has a certain amount of internal resistance. Using a voltmeter it may indicate 13.2V, which is it's typical noload voltage. When a mechanic tests the battery he connects a device which has a high resistance (the voltmeter) in parallel with a large, high wattage load resistor. There is a switch which must be depressed to connect the load resistor to the battery. The purpose of that is to simulate the starter motor. By pressing the switch, a low resistance is paralleled with the voltmeter, and the voltmeter will indicate if the battery is good or not. Too much internal resistance means the voltage drops below an acceptable level, because there is not enough power available due to the internal resistance of the battery being too high, meaning the car may not start. (This is the typical reason why batteries or dry cells die: The internal resistance of the cell increases to a point where the voltage available under load is insufficient to power the device.)
In DCC, two things can happen with poor wiring or no bus wiring. The decoder can overheat from excessive current draw, damaging or destroying it. Or the circuit breaker may not work as intended, failing to trip on an over current event can mean damaged locomotives or even wheels being welded to the track.
During the wiring phase, the track should be tested regularly. One test is the Quarter Test, named because a coin is placed across the rails. The booster should cut out immediately. If not, there is a problem with the wiring. Correct it before any damage happens.
Voltage Drop caused by Rail Resistance
One of the reasons for using a track bus with multiple feed points is to reduce the resistance presented by the rail. Compared to an equivalent copper wire, Nickel Silver has 19 times the resistance. Nickel Silver is a copper alloy (60%), with the remainder being equal amounts of nickel and zinc.
By running a lower resistance copper wire in parallel with a higher resistance wire (such as rail) Ohm's Law states that the resistance is 1/R_{total} = 1/R_{1} + 1/R_{2} . Effectively making the resistance of the pair almost equal to the value of the lower resistance copper wire.
By not relying on the rail to carry current, voltage drop is minimized by allowing current to move to the site where it is needed using a lower resistance copper bus wire.
 For more information on resistance of nickel silver rails, see the Rail Size page.
Example:
5m length of Nickel Silver C100 rail 5m 14AWG copper wire.
Rail = 0.4Ω Copper = 0.05Ω
Equivalent resistance: Rail = 1/0.4 = 2.5 Copper = 1/0.05 = 20
This formula can also be expressed at R_{Total} = (R_{1}^{1} + R_{2}^{1})^{1}
X^{1} is the same as 1/x.
Sum of the two values is 22.5, result of 1/22.5 = 0.044 Ω
This formula can also be expressed at R_{Total} = (R_{1}^{1} + R_{2}^{1})^{1}
X^{1} is the same as 1/x.
Voltage Drop (DC Resistance)
Rail = 0.4Ω X 2.5A = 1V
Copper Wire 0.05Ω X 2.5A = 125mV
Rail plus Copper wire in parallel: 0.044Ω X 2.5A = 0.111V (111mV)
Exchanging the C100 rail for C70, the resistance increases to ~ 1Ω, so the voltage drop on the rail alone is 2.5V
Effect Without a DCC Power Bus
Relying exclusively on the rails to carry the power will introduce a significant amount of voltage drop.
Using the table below, the impedance of C100 rail is 0.076Ω per metre. If the track runs 10 metres, the impedance is 0.76Ω X 2, or 1.52Ω. A one amp current will result in a 1.5V drop across the circuit. Placing a bus with an impedance of 0.55Ω in parallel with the track results in a total impedance of 0.4Ω
For easier math, without the power bus, at 1A V_{drop} is 1.5V, with the power bus, V_{Drop} is 0.4V. Without the Power Bus arrangement, the voltage drop is 3.75 times more.
Apply that to Code 80 rail: Z_{80} is 10 X 2 X 0.108Ω, or 20 X 0.108 = 2.16Ω. At one amp, V_{Drop80} = 1A X 2.16Ω = 2.16V. Multiply that by 5A and V_{Drop80} is now 10.8V.
Voltage Drop AC Measurements
Since the rail impedance is an AC measurement, it would be better to use AC equivalents for the power bus too. An Ohmmeter only measures the DC resistance, it doesn't see any inductance or capacitance present. Due to the nature of the DCC Waveform, the booster sees the track and power bus as an impedance, which is much larger than the DC resistance of the circuit. See Track Bus Impedance for more details on the power bus measurements.
The power bus is 12AWG and has an impedance of 0.55Ω/10m loop, or 20m total. (0.55^{1} = 1.8.)
Rail Size (Code)  Rail Impedance  Bus Impedance  Total Z Bus//Rail  Both Legs  Voltage Drop at 1 Amp 

100  0.76  0.4  0.3  0.5  0.5 
83  1.08  0.4  0.3  0.6  0.6 
70  2.06  0.4  0.3  0.7  0.7 
 Calculated as follows:
 Length of power district is 10 metres
 Bus is estimated at 0.4 Ω per line
 Rail and Bus are connected in parallel, with the bus value stated above
 The result is doubled to represent the sum of both legs of the circuit
 The Voltage Drop is simply the total impedance multiplied by 1A. Multiply by 5 to see a value at 5A.
 For 1A to flow in the circuit, the sum of the loads across the booster outputs would be equal to Volts ÷ Amps
 These are worst case scenarios. Most of the time your current draw will not be 5A in a given power district.
 Recommended maximum V_{Drop} for DCC Wiring should be 5%, not exceeding 10%.
Assuming HO scale with 15V on the rails, the maximum permissible voltage drop is 10%, or 1.5V. At 5% this value is 0.75V
Code 100
Using the results found above, the C100 results at 5A exceed V_{Dropmax} of 1.5V. The same applies to C83 and C70 rail. At a lower current, such as 2A, the voltage drop is within the permissible maximum of 1.5V at V. It is also close to the value for V_{Drop5%} at 0.8V.
Code 83
The V_{drop} for Code 83 at 5A exceeds V_{Dropmax}, but it is acceptable at 2A with a V_{drop} of 1.0V.
Notes on Voltage Drop
If you were to place a load at the end of the track (the 10m point) which causes a draw of 5A total, measuring across that load:
V_{Load} = V_{source} − (V_{DropA} + V_{DropB})
Example:
 V_{source} =15V
 V_{DropA} = 1V
 V_{DropB} = 1V
V_{Load} = 15V − (1V + 1V) = 15 − 2 = 13V
Using this example, while you may measure 15V at the booster output, there will be 13V at the load. As the power (volts X amps) must stay constant, as the voltage drops the current increases.
(The total voltage must equal the sum of all the voltage drops.)
As seen through the various calculated examples, the lighter the rail, the heavier the power bus must be to counteract the increased impedance of the rail. Doing so reduces the Voltage Drop to a value within acceptable limits. This becomes more important in smaller scales with lower track voltages.
Scale  Recommended Track Voltage  V_{Drop5%}  V_{Drop10%} 

N  12V  0.6V  1.2V 
HO  15V  0.75V  1.5V 
O  20V  1.0  2.0V 
Rail Impedance
See page Rail Size for more details on the resistance of Nickel Silver Rail.
Code of Rail  Impedance per metre, mΩ 

100  76 
83  108 
70  206 
Rail resistance measurement accuracy is >100ppm.
Different alloys and rail profiles will have different resistance values.
See Also
 Wiring  General wiring
 Wire sizes and spacing  Guidelines to determining wire sizes
 More information of wire gauges, see the Wikipedia entry: American Wire Gauge, or for British sizing, Standard Wire Gauge