Lesson 5: Calculating Voltage Drop in Feeders and Branch Circuits

Question 1

What size copper conductors are needed to supply a 3-phase, 208-volt, 200-ampere load at a distance of 250 feet and not exceed a 3% voltage drop?

Use k = 12.9.

a.
2/0 AWG

b.
3/0 AWG

c.
4/0 AWG

d.
250 kcmil

Answer 1

c. 4/0 AWG

Note:
Vdmax = supply voltage × 3%
= 208 × 0.03
= 6.24 V

cmils = (k × L × I × 1.73) ÷ Vd
= (12.9 × 200 × 250 × 1.73) ÷ 6.24
= 1,115,850 ÷ 6.24
= 178,822 cmils
Chapter 9, Table 8, Area, cmils
Read (more than) 178,822 = 211,600 cmils
211,600 cmils = 4/0 AWG copper

Question 2

How much greater is the resistance in ohms per 1,000 feet (Ω/kFT) of an uncoated 10 AWG stranded copper conductor than that of a 10 AWG solid copper conductor?

a.
0.01 Ω/kFT

b.
0.02 Ω/kFT

c.
0.03 Ω/kFT

d.
0.04 Ω/kFT

Answer 2

c. 0.03 Ω/kFT

Question 3

What is the voltage drop on a single-phase, 240-volt branch circuit supplying a 100-ampere load at a distance of 105 feet with 1 AWG THWN aluminum conductors? (Round the FINAL answer to two decimal places.)

Answer 3

5.32 V

Note:
Chapter 9, Table 8, DC resistance
1 AWG THWN aluminum = 0.253 Ω/kFT
Vd = (DC Resist. × I × 2L) ÷ 1,000
= (100 × 2 × 105 × 0.253) ÷ 1,000
= 5,313 ÷ 1,000
= 5.313 V

Question 4

How much larger is the diameter of an 8 AWG stranded conductor than that of an 8 AWG solid conductor?

a.
0.014”

b.
0.018”

c.
0.021”

d.
0.024”

Answer 4

b.
0.018”

Question 5

What is the voltage drop on a single-phase, 460-volt branch circuit supplying a 215-ampere load at a distance of 118 feet, with 4/0 AWG THWN copper uncoated conductors at maximum operating temperature? (Round the FINAL answer to three decimal places.)

Answer 5

3.097 V

Note:
Chapter 9, Table 8, DC resistance
4/0 AWG uncoated copper = 0.0608 Ω/kFT
Vd = (DC Resist. × I × 2L) ÷ 1,000
= (0.0608 × 215 × 2 × 118) ÷ 1,000
= 3,084.992 ÷ 1,000
= 3.085 V

Question 6

What is the voltage drop on a single-phase, 208-volt branch circuit supplying a 130-ampere load at a distance of 185 feet with 2/0 AWG THWN aluminum conductors? (Round the FINAL answer to two decimal places.)

Answer 6

7.66 V

Note:
Chapter 9, Table 8, DC resistance
2/ 0 AWG THWN aluminum = 0.159 Ω/kFT
Vd = (DC Resist. × I × 2L) ÷ 1,000
= (0.159 × 130 × 2 × 185) ÷ 1,000
= 7,647.9 ÷ 1,000
= 7.65 V

Question 7

What is the resistance of 500 feet of 250,000 circular mils uncoated copper? (Round the FINAL answer to five decimal places.)

Answer 7

0.02575 ohms

Note:

Chapter 9, Table 8, DC resistance

250 kcmil uncoated copper = 0.0515 Ω/kFT
R = (DC Res. × L) ÷ 1,000

= (0.0515 × 500) ÷ 1,000

= 25.75 ÷ 1,000

= 0.02575 Ω

Question 8

What minimum size copper wire is needed for a 120-volt, single-phase branch circuit supplying a 30-ampere load at a distance of 205 feet to limit the voltage drop within the recommended Code limit?
Use k = 12.9.

Answer 8

3 AWG

Note:
210.19(A), Informational Note No. 3

Voltage drop limit = 3%
Vd = supply voltage × 3%
= 120 × 0.03
= 3.6 V

cmils = (k × I × 2L) ÷ Vd
= (12.9 × 30 × 2 × 205) ÷ 3.6
= 158,670 ÷ 3.6
= 44,075 cmils

Chapter 9, Table 8, Area, cmils
Read (more than) 44,075 = 52,620 cmils

52,620 cmils = 3 AWG copper

Question 9

What is the maximum length of a single-phase, 120-volt branch circuit supplying a 10-ampere load with 14 AWG solid copper conductors permitted without exceeding a voltage drop of 3.6 volts? (Round the FINAL answer to two decimal places.)

Answer 9

58.63 ft

Note: Since K is not given, use Chapter 9, Table 8 values.

Vd=IxR

=Ix  (2xLxDC resist.)/1000

L =(Vdx1000)/Ix2xDC resist.

=(3.6x1000)/10x2x3.07

=3600/61.4

=58.63192

Question 10

What is the maximum current for a single-phase, 230-volt branch circuit supplying a load at a distance of 140 feet with 4 AWG copper conductors and holding the voltage drop to 4.6 volts? (Round the FINAL answer to two decimal places.)
Use k = 12.9.

Answer 10

53.15 A

Note:

Chapter 9, Table 8, circular mils 4 AWG copper = 41,740 circular mils
Imax = (circular mils × Vd) ÷ (k × 2L)

= (41,740 × 4.6) ÷ (12.9 × 2 × 140)

= 192,004 ÷ 3,612

= 53.16 A

Question 11

What is the voltage drop on a single-phase, 208-volt branch circuit supplying a 54-ampere load at a distance of 98 feet using 6 AWG RHW uncoated copper conductors at maximum operating temperature? (Round the FINAL answer to two decimal places.)

Answer 11

5.21 V

Note:
Chapter 9, Table 8, DC resistance
6 AWG copper = 0.491 Ω/kFT
Vd = (DC res. × I × 2L) ÷ 1,000
= (0.491 × 54 × 2 × 98) ÷ 1,000
= 5,197 ÷ 1,000
= 5.20 V

Question 12

What is the resistance of 200 feet of 8 AWG coated solid copper conductor? (Round the FINAL answer to four decimal places.)

Answer 12

0.1572 ohms

Note:

Chapter 9, Table 8, DC resistance

8 AWG solid coated copper = 0.786 Ω/kFT
R = (DC Res. × L) ÷ 1,000

= (0.786 × 200) ÷ 1,000

= 157.2 ÷ 1,000

= 0.1572 Ω
The correct answer is: 0.1572

Question 13

What is the voltage drop on a 3-phase, 230-volt branch circuit supplying a 125-ampere load at a distance of 175 feet with 4/0 AWG THWN copper uncoated conductors? (Round the FINAL answer to two decimal places.)

Answer 13

2.3 V

Note:
Chapter 9, Table 8, DC resistance
4/0 AWG uncoated copper = 0.0608 Ω/kFT
Vd = (DC Resist. × I × 1.73L) ÷ 1,000
= (0.0608 × 125 × 1.73 × 175) ÷ 1,000
= 2,300.9 ÷ 1,000
= 2.30 V

Question 14

What is the maximum length of a single-phase, 110-volt branch circuit supplying a 40-ampere load with 6 AWG aluminum conductors permitted without exceeding a voltage drop of 3.3 volts? (Round the FINAL answer to two decimal places.)
Use k = 21.2.

Answer 14

51.05

Note:

Chapter 9, Table 8, cmils 6 AWG aluminum = 26,240 cmils
L = (cmils × Vd) ÷ (2 × k × I)

= (26,240 × 3.3) ÷ (2 × 21.2 × 40)

= 86,592 ÷ 1,696

= 51.06 ft. max. length (one way)

Question 15

What is the voltage drop on a 3-phase, 480-volt feeder supplying a 400-ampere load at a distance of 95 feet, with 500 kcmil THWN copper uncoated conductors? (Round the FINAL answer to two decimal places.)

Answer 15

1.7 V

Note:
Chapter 9, Table 8, DC resistance
500 kcmil uncoated copper = 0.0258 Ω/kFT
Vd = (DC Resist. × I × 1.73L) ÷ 1,000
= (0.0258 × 400 × 1.73 × 95) ÷ 1,000
= 1,696.092 ÷ 1,000
= 1.70 V
The correct answer is: 1.7

Question 16

What minimum size copper wire is needed for a 230-volt, single-phase branch circuit supplying a 65-ampere load at a distance of 250 feet to limit the voltage drop within the recommended Code limit?

Use k = 12.9.

Answer 16

2 AWG

210.19, Informational Note
Voltage drop limit = 3%

Vd = supply voltage × 3%
= 230 × 0.03
= 6.9 V

cmils = (k × I × 2L ) ÷ Vd
= (12.9 × 65 × 2 × 250) ÷ 6.9
= 419,250 ÷ 6.9
= 60,761 cmils

Chapter 9, Table 8, Area, cmils
Read (more than) 60,761 = 66,360 cmils
66,360 cmils = 2 AWG copper

Question 17

What is the voltage drop on a single-phase, 240-volt branch circuit supplying a 48-ampere load at a distance of 88 feet using 4 AWG RHW aluminum conductors at maximum operating temperature? (Round the FINAL answer to two decimal places.)

Answer 17

4.30 V

Note:
Chapter 9, Table 8, DC resistance
4 AWG aluminum = 0.508 Ω/kFT
Vd = (DC res. × I × 2L) ÷ 1,000
= (0.508 × 48 × 2 × 88) ÷ 1,000
= 4,290 ÷ 1,000
= 4.29 V
The correct answer is: 4.29

Question 18

Which of the following does not specifically change the DC resistance of a particular conductor?

a.
Coating

b.
Insulation

c.
Material

d.
Stranding

Answer 18

b. insulation

Question 19

What is the resistance of 300 feet of 10 AWG solid aluminum conductor? (Round the FINAL answer to two decimal places.)

Answer 19

.6 ohms

Note:

Chapter 9, Table 8, DC resistance

10 AWG solid aluminum = 2.0 Ω/kFT
R = (DC Res. × L) ÷ 1,000

= (2.0 × 300) ÷ 1,000

= 600 ÷ 1,000

= 0.60 Ω
The correct answer is: 0.6

Question 20

What is the voltage drop on a 3-phase, 480-volt branch circuit supplying a 120-ampere load at a distance of 65 feet with 1 AWG THW uncoated copper conductors at maximum operating temperature? (Round the FINAL answer to two decimal places.

Answer 20

2.08 V

Note:

Chapter 9, Table 8, DC resistance

1 AWG uncoated copper = 0.154 Ω/kFT
Vd = (DC Res. × I × 1.73L) ÷ 1,000

= (0.154 × 120 × 1.73 × 65) ÷ 1,000

= 2,080 ÷ 1,000

= 2.08 V

Question 21

What minimum size aluminum wire is needed for a 440-volt, 3-phase branch circuit supplying a 60-ampere load at a distance of 325 feet and holding the voltage drop to 13.2 volts?
Use k = 21.2

Answer 21

2 AWG

Note:

cmils = (k × L × I × 1.73) ÷ Vd

= (21.2 × 60 × 325 × 1.73) ÷ 13.2

= 715,182 ÷ 13.2

= 54,180 cmils

Chapter 9, Table 8, Area, cmils

Read (more than) 54,180 = 66,360 cmils

66,360 cmils = 2 AWG aluminum

Question 22

What is the resistance of 175 feet of 14 AWG stranded uncoated copper conductor? (Round the FINAL answer to four decimal places.)

Answer 22

.5495 ohms

Note:

Chapter 9, Table 8, DC resistance

14 AWG stranded uncoated copper = 3.14 Ω/kFT
R = (DC Res. × L) ÷ 1,000

= (3.14 × 175) ÷ 1,000

= 549.5 ÷ 1,000

= 0.5495 Ω

Question 23

A 3-phase service is 240 volts at the service equipment. Presently, there is a 5-volt drop to the downstream distribution panel. What size copper branch-circuit conductors are needed to supply a 38-ampere, 3-phase branch-circuit load at a distance of 110 feet and not exceed a total 5% voltage drop on the feeder plus the branch circuit?

Use k = 12.9.

Answer 23

8 AWG

Note:
Vdmax = supply voltage × 5%
= 240 × 0.05
= 12 V

Vd (BC) = Vdmax − Vd (feeder)
= 12 − 5
= 7 V (branch circuit)

cmils = (k × I × 1.73 × L ) ÷ Vd (BC)
= (12.9 × 38 × 1.73 × 110) ÷ 7
= 93,285.06 ÷ 7
= 13,326 cmils

Chapter 9, Table 8, Area, cmils
Read (more than) 13,326 = 16,510 cmils
16,510 cmils = 8 AWG copper

Question 24

The resistance of a conductor will change according to the ambient temperature.
true or false

Answer 24

True