# ISA Certified Automation Professional (CAP) Program

This question is from the CAP study guide, Performance Domain III, System Design.

Definition: Design, specify, and procure the hardware/software used in the system.

#### CAP question

R= r L/A

What is the resistance of 1000 ft of copper wire (specific resistance = 10.37) given a cross-sectional area of 10370 circular mil (cmil) and a wire temperature of 20°C?

A. 1 Ω

B. 2 Ω

C. 10 Ω

D. 100 Ω

#### CAP answer

The resistance of a length (L) of a conductor can be determined using the specific resistance and the cross-sectional area (A) in cmil by using the equation R = rL/A. The correct answer is A, 1 Ω.

Reference: Hughes, Programmable Controllers, ISA Press 2001.

Cmil is worth reviewing. Recall electrons flow through large-diameter wires easier than small-diameter wires, due to the greater cross-sectional area they have to move.

Rather than measure small wire sizes in inches, the unit of "mil" (1/1000 of an inch) is common. The cross-sectional area of a wire can be in terms of square units (square inches or square mils), circular mils, or gauge scale.

Calculating square-unit wire area for a circular wire involves the circle area formula:

A=πr2 (Square units)

Calculating circular-mil wire area for a circular wire is much simpler because the unit of circular mil exists just for this purpose, to eliminate the pi and the d/2 (radius) factors in the formula.

A=d2 (Circular units)

There are π (3.1416) square mils for every 4 circular mils.

Nicholas Sheble edits the Certification department. For information about the CAP program, go to www.isa.org/CAP.