NCCER Module 26104-23 PT 4

Electrical

Module 26104-23

Electrical Theory

Copyright © 2024 by NCCER, Alachua, FL 32615. Published by Pearson. All rights reserved.

1.0.0 Resistive Circuits

Module 26104-23 – Electrical Theory

Objective

1. Calculate values in resistive circuits.

a. Identify resistances in series.

b. Identify resistances in parallel.

c. Simplify series-parallel circuits.

Module 26104-23 – Electrical Theory

Performance Tasks

There are no Performance Tasks associated with this section.

Module 26104-23 – Electrical Theory

1.0.0–1.1.0 Identifying Resistances in Series

The total resistance in a series circuit equals
the sum of all the resistances.

𝑅T = 𝑅1 + 𝑅2 + 𝑅3

𝑅T = 50Ω + 75Ω + 100Ω

𝑅T = 225Ω

Module 26104-23 – Electrical Theory

1.2.0 Identifying Resistances in Parallel

•

Most practical circuits are wired in
parallel.

•

Three methods for calculating
resistances in parallel circuits:
–
Reciprocal method

–
Product-over-sum method

–
Method for equal resistances only

Module 26104-23 – Electrical Theory

1.2.1 Using the Reciprocal Formula (1 of 3)

𝑅T =
1

1
𝑅1+ 1

𝑅2+ 1

𝑅n

RT = total resistance in parallel

R1, R2, Rn = each of the branch

resistances

(Rn stands for any additional branch

resistances.)

Module 26104-23 – Electrical Theory

1.2.1 Using the Reciprocal Formula (2 of 3)

Find the total resistance of the 2Ω, 4Ω, and
8Ω resistors in parallel.

𝑅T =
1

1
𝑅1+ 1

𝑅2+ 1

𝑅3

Module 26104-23 – Electrical Theory

1.2.1 Using the Reciprocal Formula (3 of 3)

𝑅T =
1

1
2Ω+ 1

4Ω+ 1

8Ω

𝑅T =
1

0.5Ω + 0.25Ω + 0.125Ω

𝑅T =
1

0.875Ω

𝑅T = 1.14Ω

Module 26104-23 – Electrical Theory

1.2.2 Using the Product-over-Sum Formula (1 of 3)

When there are only two resistors in a
parallel circuit:

𝑅T = 𝑅1 × 𝑅2

𝑅1 + 𝑅2

Module 26104-23 – Electrical Theory

1.2.2 Using the Product-over-Sum Formula (2 of 3)

Find the total resistance of 5Ω and 10Ω resistors in parallel.

𝑅T =𝑅1 × 𝑅2

𝑅1 + 𝑅2

Module 26104-23 – Electrical Theory

1.2.2 Using the Product-over-Sum Formula (3 of 3)

Find the total resistance of 5Ω and 10Ω resistors in parallel.

𝑅T =𝑅1 × 𝑅2

𝑅1 + 𝑅2

𝑅T = 5Ω × 10Ω

5Ω + 10Ω

𝑅T = 50Ω

15Ω

𝑅T = 3.33Ω

Module 26104-23 – Electrical Theory

1.2.3 Using the Formula for Equal Resistances in Parallel

•

If resistors are equal:

𝑅T = resistance of one resistor

total number of resistors

•

Calculate equivalent values:
–

Two 200Ω resistors = one 100Ω
resistor

–

Two 100Ω resistors = one 50Ω
resistor

–

Two 50Ω resistors = one 25Ω resistor

Module 26104-23 – Electrical Theory

1.3.0 Working with Series-Parallel Circuits

To find current, voltage, and resistance
in a series-parallel circuit, apply the
correct rules for each part of the circuit.

Module 26104-23 – Electrical Theory

1.3.1 Recognizing Series and Parallel Combinations

•

Trace the paths to identify
branches and loads.

•

For more complex circuits, you
may have to redraw them, so they
are easier to recognize.

Module 26104-23 – Electrical Theory

1.3.2 Reducing Series-Parallel Circuits

•

To find total resistance, reduce
the circuit to its simplest form.

•

Apply the rules for series and
parallel circuits to combine the
values of all the resistors into a
single equivalent value.

Module 26104-23 – Electrical Theory

Trade Term

Series-parallel circuit: A circuit that contains both series and parallel current
paths.

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 1

1. You can use Ohm’s law to find the value of each branch current in a

parallel circuit.

a. True

b. False

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 1 Answer

1. You can use Ohm’s law to find the value of each branch current in a

parallel circuit.

a. True

b. False

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 2

2. Which of the following is true regarding a parallel circuit?

a. It has more than one path for current flow.

b. The resistance is the same through all circuit components.

c. The total resistance is equal to the sum of the individual resistances.

d. The current flow through each resistor is always less than the total

resistance.

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 2 Answer

2. Which of the following is true regarding a parallel circuit?

a. It has more than one path for current flow.

b. The resistance is the same through all circuit components.

c. The total resistance is equal to the sum of the individual resistances.

d. The current flow through each resistor is always less than the total

resistance.

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 3

3. Which of the following is true regarding a series-parallel circuit?

a. There is only one path for current flow.

b. The resistance is the same through all circuit components.

c. Once reduced to an equivalent series circuit, the total resistance is

found by adding the series loads.

d. The current flow through each resistor is always less than half the value

of the total resistance.

Module 26104-23 – Electrical Theory

1.0.0 Section Review Question 3 Answer

3. Which of the following is true regarding a series-parallel circuit?

a. There is only one path for current flow.

b. The resistance is the same through all circuit components.

c. Once reduced to an equivalent series circuit, the total resistance

is found by adding the series loads.

d. The current flow through each resistor is always less than half the value

of the total resistance.

Next…

2.0.0
Ohm’s and Kirchhoff’s Laws

Read Sections 2.0.0 through 2.3.0. Complete the 2.0.0 Section Review.

Electrical

Module 26104-23

Electrical Theory

Copyright © 2024 by NCCER, Alachua, FL 32615. Published by Pearson. All rights reserved.

2.0.0 Ohm’s and Kirchhoff’s Laws

Module 26104-23 – Electrical Theory

Objective

2. Apply Ohm’s and Kirchhoff’s laws to various types of circuits.

a. Use Ohm’s law to solve for unknown circuit values.

b. Explain Kirchhoff’s current and voltage laws.

c. Apply Ohm’s and Kirchhoff’s laws to solve for unknown circuit values.

Module 26104-23 – Electrical Theory

Performance Tasks

There are no Performance Tasks associated with this section.

Module 26104-23 – Electrical Theory

2.0.0–2.1.0 Ohm’s Law

•

Ohm’s law is used to calculate voltage, current, and resistance values in
circuits.

•

If you know two of the values, you can calculate the third.

Module 26104-23 – Electrical Theory

2.1.1 Applying Ohm’s Law in Series Circuits (1 of 2)

•

First, calculate total resistance:

𝑅! = 𝑅" + 𝑅# + 𝑅$

•

Next, calculate total current:

𝐼! = 𝐸!
𝑅!

Module 26104-23 – Electrical Theory

2.1.1 Applying Ohm’s Law in Series Circuits (2 of 2)

•

Use total current to find the
voltage drop (IR drop) across each
resistor:

𝐸" = 𝐼" × 𝑅"
𝐸# = 𝐼# × 𝑅#
𝐸$ = 𝐼$ × 𝑅$

•

The sum of IR drops is equal to
the total voltage (ET).

Module 26104-23 – Electrical Theory

2.1.2 Applying Ohm’s Law in Parallel Circuits (1 of 2)

•

The total current IT is equal to the sum of
all branch currents.

•

To find the current for individual branches:

𝐼" = 𝐸"
𝑅"
= 𝐸!
𝑅"

𝐼# = 𝐸#
𝑅#
= 𝐸!
𝑅#

𝐼$ = 𝐸$
𝑅$
= 𝐸!
𝑅$

Module 26104-23 – Electrical Theory

2.1.2 Applying Ohm’s Law in Parallel Circuits (2 of 2)

To find an unknown current:

𝐼! = 𝐼" + 𝐼#

𝐼# = 𝐼! − 𝐼"

𝐼# = 20A − 12A

𝐼# = 8A

Module 26104-23 – Electrical Theory

2.1.3 Applying Ohm’s Law in Series-Parallel Circuits

•

Simplify a series-parallel circuit to
a series circuit.

•

Then, total circuit resistance, total
current, and voltage drops can be
calculated.

Module 26104-23 – Electrical Theory

2.2.0–2.2.1 Kirchhoff’s Current Law

Kirchhoff’s current law states that at
any point in a circuit, the total
current entering that point must
equal the total current leaving that
point.

Module 26104-23 – Electrical Theory

2.2.2 Kirchhoff’s Voltage Law (1 of 2)

Kirchhoff’s voltage law states that the
algebraic sum of the voltages around
any closed path is zero.

𝐸! − 𝐸" − 𝐸# − 𝐸$ = 0

100V − 50V − 30V − 20V = 0

Module 26104-23 – Electrical Theory

2.2.2 Kirchhoff’s Voltage Law (2 of 2)

Work your way around the loop in
whichever direction you like.
•

If the sign is positive, treat the
component as a voltage rise.
•

If the sign is negative, treat the
component as a voltage drop.

Module 26104-23 – Electrical Theory

2.3.0 Applying Ohm’s and Kirchhoff’s Laws (1 of 5)

To calculate total resistance, first
calculate resistance in the right-hand
loop:

𝑅%&' = 𝑅% + 𝑅'

𝑅$&%&' =
1

1
𝑅$+
1
𝑅%&'

Module 26104-23 – Electrical Theory

2.3.0 Applying Ohm’s and Kirchhoff’s Laws (2 of 5)

•

Then, calculate total resistance:

𝑅! = 𝑅" + 𝑅# + 𝑅$&%&'

•

Total resistance can then be used
to calculate total current:

𝐼! = 𝐸!
𝑅!

Module 26104-23 – Electrical Theory

2.3.0 Applying Ohm’s and Kirchhoff’s Laws (3 of 5)

•

Use Ohm’s law to calculate the
voltage drops across R1 and R2:

𝐸" = 𝐼! × 𝑅"
𝐸# = 𝐼! × 𝑅#

•

Use Kirchhoff’s voltage law to
calculate voltage drop across R3:

𝐸$ = 𝐸() − 𝐸" − 𝐸#

Module 26104-23 – Electrical Theory

2.3.0 Applying Ohm’s and Kirchhoff’s Laws (4 of 5)

•

Use Ohm’s law to calculate current
flow through R3:

𝐼$ = 𝐸$
𝑅$

•

Calculate the value of I4+5

𝐼! − 𝐼$ − 𝐼%&' = 0

Module 26104-23 – Electrical Theory

2.3.0 Applying Ohm’s and Kirchhoff’s Laws (5 of 5)

•

Finally, calculate the voltage drop
through R4 and R5:

𝐸% = 𝐼% × 𝑅%

𝐸' = 𝐼' × 𝑅'

•

Check calculations with:

𝐸$ − 𝐸% − 𝐸' = 0V

Module 26104-23 – Electrical Theory

Trade Terms

Kirchhoff’s current law: The statement that the total amount of current
flowing through a parallel circuit is equal to the sum of the amounts of
current flowing through each current path.

Kirchhoff’s voltage law: The statement that the sum of all the voltage drops
in a circuit is equal to the source voltage of the circuit.

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 1

1. Two branches of a circuit (R1 and R2) across a 120V power line draw a
total line current of 30A. Branch R1 takes 15A. What is the current I2 in
branch R2?

a. 12A

b. 15A

c. 17A

d. 30A

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 1 Answer

1. Two branches of a circuit (R1 and R2) across a 120V power line draw a
total line current of 30A. Branch R1 takes 15A. What is the current I2 in
branch R2?

a. 12A

b. 15A

c. 17A

d. 30A

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 2

2. Who stated that the current entering a point must equal the total current
leaving that point?

a. Kirchhoff

b. Joule

c. Pascal

d. Ohm

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 2 Answer

2. Who stated that the current entering a point must equal the total current
leaving that point?

a. Kirchhoff

b. Joule

c. Pascal

d. Ohm

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 3

3. Kirchhoff’s voltage law can be used to check calculations made using
Ohm’s law.

a. True

b. False

Module 26104-23 – Electrical Theory

2.0.0 Section Review Question 3 Answer

3. Kirchhoff’s voltage law can be used to check calculations made using
Ohm’s law.

a. True

b. False

Next…

Review for Module Testing

Complete the Review Questions at the end of the module and prepare
for the Module Test.