Calculating Conductor Size

The previous problem was used to illustrate the principle of voltage drop. In practice, because the percent of drop is fixed by electrical codes, conductors are sized by calculating the amount of resistance per 1,000 ft that will result in an acceptable voltage drop, and then selecting the appropriate size of wire from a table similar to Appendix XII.

Problem: What size of wire is needed to carry a 120-V, 15.0-amp load with a 2% drop when the run is 200.0 ft?

Solution: The first step is to determine the permissible amount of voltage drop:

The second step is to determine the amount of resistance for the load that will cause a 2.4-V drop. This is accomplished by using Ohm's law:

I 15.0 amp

For a circuit with a resistance of less than 0.16 ^ and a load of 15.0 amps the voltage drop will be less than 2%. Remember that the voltage used to calculate the resistance is the voltage drop, not the source voltage.

To select the correct size wire the calculated circuit resistance must be converted to units of ^/1,000 ft, and then select the appropriate wire size from Appendix XII. This can be accomplished using units cancellation.

x 1,000 ft

1,000 ft Run

Next, compare this value to the resistance values in Appendix XII. The objective is to select a size of wire with a resistance equal to or less than the calculated value. From Appendix XII, the resistance of No. 6 wire is 0.41 ^/1,000, and the resistance of No. 4 wire is 0.26 ^/1,000 ft. The No. 4 wire would be the best choice as the resistance is closest to the calculated resistance without being larger.

These examples illustrate the principle that voltage drop is caused by resistance and current. Another example of the importance of understanding voltage drop is in the use of extension cords. Improper use of extension cords can lead to serious consequences. Many extension cords sold in retail stores use No. 16 or No. 18 wire. Extension cords of this size are very limited in current carrying capacity. Also, when more than one extension cord is used, the resistance of the connection can be equal or greater than the resistance of the wire. This is why the connections of an extension cord that has been overloaded will be warm or hot to the touch.

Problem: What size load (amp) can a 100.0-ft, No. 18 extension cord carry on a 120 V circuit without exceeding a 2% voltage drop?

Solution: The first step is to determine the allowable voltage drop:

The next step is to determine the amount of current that will cause a 2.4-V drop in the extension cord. This is accomplished by using Ohm's law and the resistance of No. 18 wire. Remember to use two times the length (100.0 ft x 2 = 200.0 ft) to determine the total feet of conductor.

E 2.4 V 2.4 V E = IR I = - = -=-= 1.843... or 1.84 amp

1,000 ft

The maximum electrical load for a 100 ft, No. 18 extension cord is 1.84 amps. If the extension cord is used for a larger load (more amps), it will overheat.

An often unrecognized factor when using extension cords is the resistance of the connections. Two 50-ft extension cords may have more resistance than a 100 ft cord with the same size of conductors. To more clearly understand the potential problem with extension cords, consider the following example.

Problem: What is the maximum capacity of the No. 18 extension cord in the previous problem if two 50-ft cords are used, and the connection has a resistance of 8.0 W?

Solution: Using an allowable voltage drop of 2.4 V and Ohm's law:

9.302 W

This example shows that using two 50-ft extension cords instead of one 100-ft cord reduces the capacity by seven times when the connection resistance is 8.0 ohms because of the additional resistance of the connection.

Many appliances are rated in watts. To determine the size of conductors required to supply an appliance rated in watts, the electrical power (watts) must be used first to determine the load in amps.

Problem: A 25.0-ft extension cord will be used to operate a 1,100-W, 120-V electrical iron. What size of extension cord should be selected?

Solution: The first step is to determine the amperage used by the iron.

E 120 V

Using an allowable voltage drop of 2%, the next step is to determine total allowable resistance:

I 9.27 amp

The total allowable resistance in the extension cord is 0.26 W. The next step is to determine the ohms of resistance per 1,000 ft:

The resistance of a No. 18 wire is 6.51 ft/1,000 ft, and that of a No. 16 wire is 4.09 ft/1,000 ft. Assuming the iron and cord connectors are in good condition, a 25-ft extension cord with No. 16 wire is adequate for the 1,100-W iron.