Calculating Voltage Drop

To maintain the heat produced by electricity passing through a resistance at the designed level, national standards, primarily the National Electric Code, limit the voltage drop allowed in a circuit. For most circuits this is 2 or 3%. Voltage drop is the term used to describe the reduction in voltage that occurs as electricity flows through a resistance. Voltage drop occurs because materials resist the flow of electricity; the critical issue is to ensure it does not become excessive. The amount of voltage drop is determined by the amount of current and the total resistance in the circuit. The size of a conductor required for an electrical load is determined by the allowable voltage drop for the circuit, the size of the load, and the length of wire from the source of electricity to the load. The resistance of conductors usually is listed as ohms (a) per 1,000 ft of conductor length. Because the electricity must pass through the entire length of a conductor, conductors perform as one continuous series resistance.

Appendix XII includes the resistance for various sizes of copper wire using AWG sizes and Appendix XIII contains resistance values for SI wire sizes. Notice that the resistance is given in ohms/1,000 ft or ohms/100 m. Bare wire is seldom used in circuits, but because the type of insulation used influences the resistance, these values are used to illustrate the principles of voltage drop. Resistance values for wires with different types of insulation can be found in the National Electrical Code (NEC) or other sources and these must be used when calculating wire size for a specific application.

The voltage drop is calculated using Ohm's law. For general purpose circuits, the voltage drop must be limited to 2%. The NEC allows a 3% drop for some individual circuits. In calculating voltage drop, the length of conductor usually will be measured as either the length of wire from the source to the load and back (length of wire), or the run (the distance from the source to the load).

Problem: What is the voltage drop in a wire length of 1,500.0 ft, when No. 12 wire is used, and the load is 10.0 amps?

Solution: Using Ohm's law and, from Appendix XII, using a resistance for No. 12 wire of 1.62 a/1,000 ft, the voltage drop is:

The 1,500.0 ft of No. 12 wire has a voltage drop of 24.3 V. If the source voltage is 120 V, is this an acceptable voltage drop?

120 V

The answer then is no—a 20.25% voltage drop is excessive. If No. 12 wire is used with this load, the electrical appliance will not operate correctly, the conductors will over heat and there is the potential for a fire. A larger conductor size is needed to carry a load of 10.0 amps for a distance of 1,500.0 ft.

For wires longer or shorter than 1,000 ft, the resistance is proportional to the length. The total resistance for any length is:

RL = —x L(ft) L 1,000 ft where RL = Resistance in ohms (a) for any length (ft); R = Resistance per 1,000 ft (a); L = Length of wire (ft).

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