Question

Determine the gauge of the wire needed in circuits that specify power source, wire length, amps, and maximum volt drop.

Part I
Locate the wire-size engineering reference table (Chart 44-2) of your textbook to determine wire gauge when the diameter of the wire is known.

Use the table to determine the wire gauge for each wire diameter shown below. You may need to round the numbers to obtain the correct answer.
d = 2576 inch
d = 0.03196 inch
d = 0.0100 inch
d = 0.1285 inch
d = 0.0508 inch
Using the answers you just obtained, place the wire sizes in order from the smallest gauge to the largest.
Remember: The smaller the wire gauge, the larger the diameter of the wire.

Part II
Using what you’ve learned in Part I and the directions below, determine the recommended wire gauge for the following circuits:

Circuit A. Starter circuit using 5 feet of wire, with a 12 V power supply, and a current of 200 Amps.
Circuit B. Dome light circuit using 14 feet of wire, with a 12 V power supply, and a current of 10 Amps.
Circuit C. A/C blower circuit using 24 feet of wire, with a 14.6 V power supply, and a current of 18 Amps.
Use Ohm’s law (E = IR) to determine the resistance in the wire for each circuit. Remember, Volts = E, and the given current = I. (You can refer back to page 433 in your textbook to find the exact formula you’ll need to use.)
Circuit A: R =
Circuit B: R =
Circuit C: R =
The relationship between the resistance and the circuit’s wire is shown in this formula:

R=4ρπ(Id2)
To determine the diameter of the wire needed for each circuit when you know the resistance and wire length, you would use this formula:

R=4ρπ(Id2) d=IR√×π4ρ
R = resistance

r = 250 ohm/inch

l = length of the wire (inches)

d = cross-sectional area of the wire (in2)

You should substitute the calculated value for R and the given values for r and l and find the value of d for each circuit. (Use π = 3.1416.)

For example, here’s an example for Circuit A:

d=IR√×π4ρ=5.24494×3.14161000=.064


Circuit A: d =
Circuit B: d =
Circuit C: d =
Now, look in the engineering reference table for standard American wire or metric gauges (on page 468 of your textbook) to determine the gauge of wire needed for the circuit.
Circuit A:
Circuit B:
Circuit C:

Answer 1

See below.

Step-by-step explanation:

Part I

Using Chart 44-2 in the textbook, we can determine the wire gauge for each given diameter

For d = 0.2576 inch, the wire gauge is 2 AWG.

For d = 0.03196 inch, the wire gauge is 20 AWG.

For d = 0.0100 inch, the wire gauge is 30 AWG.

For d = 0.1285 inch, the wire gauge is 8 AWG.

For d = 0.0508 inch, the wire gauge is 16 AWG.

Ordering the wire sizes from smallest to largest gauge, we have:

30 AWG < 20 AWG < 16 AWG < 8 AWG < 2 AWG

Part II

Circuit A

Using Ohm's law, we can calculate the resistance in the wire:

R = E/I = 12/200 = 0.06 ohms

Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:

d = sqrt(R/(4ρπI)) = sqrt(0.06/(42503.1416*200)) = 0.064 inches

Using the engineering reference table, we can see that the wire gauge needed for Circuit A is 2 AWG.

Circuit B

Using Ohm's law, we can calculate the resistance in the wire:

R = E/I = 12/10 = 1.2 ohms

Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:

d = sqrt(R/(4ρπI)) = sqrt(1.2/(42503.1416*10)) = 0.023 inches

Using the engineering reference table, we can see that the wire gauge needed for Circuit B is 14 AWG.

Circuit C

Using Ohm's law, we can calculate the resistance in the wire:

R = E/I = 14.6/18 = 0.811 ohms

Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:

d = sqrt(R/(4ρπI)) = sqrt(0.811/(42503.1416*18)) = 0.060 inches

Using the engineering reference table, we can see that the wire gauge needed for Circuit C is 4 AWG.