Chapter 4, Problem 35R

A 120-volt branch circuit supplies a resistive heating load of 10 amperes. The distance from the panel to the heater is approximately 140 ft. Calculate the voltage drop using (a) 14 AWG, (b) 12 AWG, (c) 10 AWG, (d) 8 AWG copper conductors. See 210.19(A), Informational Note No. 4 and 215.2(A)(1), Informational Note No. 2.

To determine

Find the value of voltage drop in 14 AWG copper wire.

Answer to Problem 35R

The obtained value of voltage drop in 14 AWG copper wire is $\underset{\_}{8.79\text{Volts drop}}$.

Explanation of Solution

Given data:

Supply voltage is 120-volt.

Current is 10 A.

The distance between panel and heater is approximately 140 ft.

14 AWG copper conductor.

Calculation:

Write the expression for voltage drop in single-phase circuit.

${\text{E}}_{\text{d}}=\frac{\text{K}\times \text{I}\times \text{L}\times 2}{\text{CMA}}$ (1)

Here,

${\text{E}}_{\text{d}}$ is the voltage drop,

K is the approximate resistance in ohms per circular-mil foot at $75°\text{C}$. The value of K for uncoated copper wire is $12.9$ and for aluminum wire is $21.2$.

I is the current, and

CMA is cross-sectional area of the conductors.

Modify Equation (1) for 14 AWG copper wire.

${\text{E}}_{\text{d}\left(14\text{AWG}\right)}=\frac{\text{K}\times \text{I}\times \text{L}\times 2}{{\text{CMA}}_{\left(14\text{AWG}\right)}}$ (2)

Refer TABLE 4-7 in the textbook for circular mil area (CMA) for many of the common conductors.

The value of CMA for 14 AWG is 4110.

Substitute $12.9$ for K, 10 A for I, 140 ft for L, and 4110 for ${\text{CMA}}_{\left(14\text{AWG}\right)}$ in Equation (2) to find the voltage drop in 14 AWG copper wire.

$\begin{array}{c}{\text{E}}_{\text{d}\left(14\text{AWG}\right)}=\frac{12.9\times 10\times 140\times 2}{4110}\\ =8.788\text{Volts drop}\\ \cong 8.79\text{Volts drop}\end{array}$

Conclusion:

Thus, the obtained value of the voltage drop for 14 AWG copper wire is $\underset{\_}{8.79\text{Volts drop}}$.

To determine

Find the value of voltage drop in 12 AWG copper wire.

Answer to Problem 35R

The obtained value of the voltage drop for 12 AWG copper wire is $\underset{\_}{5.53\text{Volts drop}}$.

Explanation of Solution

Given data:

12 AWG copper conductor.

Calculation:

Modify Equation (1) for 12 AWG copper wire.

${\text{E}}_{\text{d}\left(12\text{AWG}\right)}=\frac{\text{K}\times \text{I}\times \text{L}\times 2}{{\text{CMA}}_{\left(12\text{AWG}\right)}}$ (3)

Refer TABLE 4-7 in the textbook for circular mil area (CMA) for many of the common conductors.

The value of CMA for 12 AWG is 6530.

Substitute $12.9$ for K, 10 A for I, 140 ft for L, and 6530 for ${\text{CMA}}_{\left(12\text{AWG}\right)}$ in Equation (3) to find the voltage drop in 12 AWG copper wire.

$\begin{array}{c}{\text{E}}_{\text{d}\left(12\text{AWG}\right)}=\frac{12.9\times 10\times 140\times 2}{6530}\\ =5.531\text{Volts drop}\\ \cong 5.53\text{Volts drop}\end{array}$

Conclusion:

Thus, the obtained value of voltage drop for 12 AWG copper wire is $\underset{\_}{5.53\text{Volts drop}}$.

To determine

Find the value of voltage drop in 10 AWG copper wire.

Answer to Problem 35R

The obtained value of voltage drop for 10 AWG copper wire is $\underset{\_}{3.48\text{Volts drop}}$.

Explanation of Solution

Given data:

10 AWG copper conductor.

Calculation:

Modify Equation (1) for 10 AWG copper wire.

${\text{E}}_{\text{d}\left(10\text{AWG}\right)}=\frac{\text{K}\times \text{I}\times \text{L}\times 2}{{\text{CMA}}_{\left(10\text{AWG}\right)}}$ (4)

Refer TABLE 4-7 in the textbook for circular mil area (CMA) for many of the common conductors.

The value of CMA for 10 AWG is 10,380.

Substitute $12.9$ for K, 10 A for I, 140 ft for L, and 10,380 for ${\text{CMA}}_{\left(10\text{AWG}\right)}$ in Equation (4) to find the voltage drop in 10 AWG copper wire.

$\begin{array}{c}{\text{E}}_{\text{d}\left(10\text{AWG}\right)}=\frac{12.9\times 10\times 140\times 2}{10,380}\\ =3.479\text{Volts drop}\\ \cong \text{3}\text{.48}\text{Volts drop}\end{array}$

Conclusion:

Thus, the obtained value of voltage drop for 10 AWG copper wire is $\underset{\_}{3.48\text{Volts drop}}$.

To determine

Find the value of the voltage drop in 8 AWG copper wire.

Answer to Problem 35R

The obtained value of the voltage drop for 8 AWG copper wire is $\underset{\_}{2.19\text{Volts drop}}$.

Explanation of Solution

Given data:

8 AWG copper conductor.

Calculation:

Modify Equation (1) for 8 AWG copper wire.

${\text{E}}_{\text{d}\left(\text{8AWG}\right)}=\frac{\text{K}\times \text{I}\times \text{L}\times 2}{{\text{CMA}}_{\left(\text{8AWG}\right)}}$ (5)

Refer TABLE 4-7 in the textbook for circular mil area (CMA) for many of the common conductors.

The value of CMA for 8 AWG is 16,510.

Substitute $12.9$ for K, 10 A for I, 140 ft for L, and 16,510 for ${\text{CMA}}_{\left(\text{8AWG}\right)}$ in Equation (5) to find the voltage drop in 8 AWG copper wire.

$\begin{array}{c}{\text{E}}_{\text{d}\left(\text{8AWG}\right)}=\frac{12.9\times 10\times 140\times 2}{16,510}\\ =2.187\text{Volts drop}\\ \cong \text{2}\text{.19}\text{Volts drop}\end{array}$

Conclusion:

Thus, the obtained value of the voltage drop for 8 AWG copper wire is $\underset{\_}{2.19\text{Volts drop}}$.