Calculating Voltage Drop
3. Putting Numbers to the Problem
Okay, time to put on our math hats! Don't worry, it's not as scary as it sounds. Calculating voltage drop involves a simple formula that takes into account the factors we just discussed: resistance, length, and current. Let's break it down.
The basic formula for calculating voltage drop is: Voltage Drop (VD) = Current (I) x Resistance (R). Easy enough, right? The catch is that the resistance (R) in this formula refers to the resistance of the wire itself, and it depends on both the wire's material (usually copper or aluminum) and its size (gauge). To find the resistance of the wire, you'll typically need to consult a wire resistance chart, which provides the resistance per foot (or per 1000 feet) for different wire gauges and materials.
A more practical formula, especially for longer runs, incorporates the length of the wire: VD = 2 x K x I x D / CM. Here's what each letter represents: VD is voltage drop, K is the constant for the conductor material (12.9 for copper, 21.2 for aluminum), I is the current in amps, D is the one-way distance in feet, and CM is the circular mils of the wire. Circular mils are a unit of measurement for the cross-sectional area of a wire, and you can find them in wire size charts.
Let's look at a simple example. Suppose you have a 100-foot run of 12-gauge copper wire carrying 15 amps. Using the second formula, VD = (2 12.9 15 100) / 6530. This gives us a voltage drop of approximately 5.9 volts. If your source voltage is 120 volts, the voltage at the end of the wire would be 114.1 volts. To determine if this is acceptable, calculate the percentage voltage drop: (5.9 / 120) 100 = 4.9%. Since this is below the recommended 3% for branch circuits, the 12-gauge wire is likely suitable. If, however, the percentage was above 3%, you'd want to increase the wire gauge.
Online voltage drop calculators can be valuable tools for these calculations. Just enter the wire gauge, material, current, and distance, and the calculator will do the math for you. These calculators are a great way to quickly compare different wire sizes and see the impact on voltage drop.