１. Preface to the English version

2. Supplementary exercises for the book

1. Preface to the English version

This book is for teachers who want to teach junior high school students
about electricity calculation problems in an easy-to-understand manner.

The origin of this book is as follows.

Japanese junior high school students have a survey result that they are
the weakest in electrical calculation in all science fields. The writer
has been teaching them about electricity for about thirty years, and the
writer realizes they're not good at electricity because they can't see
electricity.

If someone could personify the invisible behavior of electricity, they
would be able to empathize, understand the meaning of electricity's formula,
and be interested in electricity. Based on this policy, the writer has
continued to improve personified models to this day. Finally, the writer completed the "vending machine / runners model",
or "VMR model".

Let me give an example using VMR model.

There is a closed circuit that consists of 1 power supply ( 6 [V] ) and
1 resistor ( 2 [Ω] ). This is a basic circuit represented by Ohm's law
( voltage 6 [V] = current 3 [A] × resistance 2 [Ω] ). VMR model personifies
this circuit as follows.

First, the electric current ( 3 [A] ) is personified as 3 runners. The
conductor that connects the power supply and the resistor is converted
into the road on which the runners run. The voltage ( 6 [V] ) is converted
into 6 cakes supplied from the vending machine per runner. A resistor (
2 [Ω] ) is converted into a tunnel with a length of 2m and a cross-sectional
area of 1 u.

In addition, VMR model converts these into the following story that "runners eat the cakes from the vending machine, then go around the road and tunnel, and return to the original vending machine on empty stomachs".

@ First, 3 runners (3 [A] ) eat 6 cakes ( 6 [V] ) supplied from a vending
machine per runner and start off vigorously. Then they run on the road
without the tunnel, and their cakes are not consumed there.

A Then they enter the 2m tunnel ( resistor 2 [Ω] ). As they pass through
the tunnel, one runner experiences collisions proportional to the number
of runners ( 3 [A] ) and frictional resistance proportional to the length
of the tunnel wall ( 2 [Ω] ). As a result, one runner consumes 6 cakes
( = 3 [A] ×2 [Ω] ) in the tunnel.

B Finally they endure hunger and arrive at the original vending machine.

C After that, they continue to run this one lap road repeatedly until cakes
in the vending machine are gone.

In this way, students can easily understand ( 6 [V] = 3 [A] × 2 [Ω] )
by imagining a runner running on an electric circuit.

In the same way, the writer described the calculation of electric power
and electric energy in this book.

Japanese junior high school students are not good at calculating electricity
because electricity is invisible. The writer thinks that applies to junior
high school students all over the world. The writer is convinced that the
"vending machine / runners model" is accepted by the students
all over the world and will improve their grades. This conviction made
me translate this book into English.

Mamoru Morita

September 2020

Contents：

Chapter 1 Current Chapter 2 Voltage Chapter 3 Resistor Chapter 4 Voltage drop Chapter 5 Ohm's law and circuit calculation Chapter 6 Electric power Chapter 7 Electric energy

● Example 1-Practice 1 In the figure on the left, 5 [A] and 3 [A] merge and a [A] is flowing.
In the figure on the right, 6 [A] is divided into 1 [A] and b [A]. Find
the current values of a and b. Figure 1-2

Example 1-Practice 2 In the figure on the left, 5 [A] and 3 [A] merge and a [A] is flowing.
In the figure on the right, 6 [A] is divided into 1 [A] and b [A]. Find
the current values of a and b. Figure 1-2

Example 1-Practice 3 In the figure on the left, 5 [A] and 3 [A] merge and a [A] is flowing. In the figure on the right, 6 [A] is divided into 1 [A] and b [A]. Find the current values of a and b. Figure 1-2

Answer: Example 1-1, a = 8, b = 8. Examples 1-2, a = 18, b = 7. Example 1-3,
a = 9, b = 5.

● Example 2-Practice 1 In the figure on the left, there are power supplies connected in series
(10, 10, 8 [V] in order from the left). The figure on the right shows a
power supply with the same voltage of 2 [V] connected in parallel. Find
the voltages a [V] and b [V]. (← is the direction of current) Fig. 2-3

Example 2-Practice 2 In the figure on the left, there are power supplies connected in series (9, 6, 4 [V] in order from the left). The figure on the right shows a power supply with the same voltage of 4.5 [V] connected in parallel. Find the voltages a [V] and b [V]. (← is the direction of current) Fig. 2-3

Example 2-Practice 3 In the figure on the left, there are power supplies connected in series
(20, 55, 25 [V] in order from the left). The figure on the right shows
a power supply with the same voltage of 12 [V] connected in parallel. Find
the voltages a [V] and b [V]. (← is the direction of current) Fig. 2-3

Answer: Example 2-Practice 1, a = 28, b = 2. Example 2-Practice 2, a = 19, b
= 4.5. Example 2-Practice 3, a = 100, b = 12.

● Example 3-Practice 1 There is a circuit in which resistors are connected in series (2, 5, 3
[Ω] in order from the left). Find the magnitude of the combined resistance
a [Ω]. (→ is the direction of current) Fig. 3-2

Example 3-Practice 2 There is a circuit in which resistors are connected in series (10, 20,
15 [Ω] in order from the left). Find the magnitude of the combined resistance
a [Ω]. (→ is the direction of current) Fig. 3-2

Example 3-Practice 3 There is a circuit in which resistors are connected in series (50, 150,
200 [Ω] in order from the left). Find the magnitude of the combined resistance
a [Ω]. (→ is the direction of current) Fig. 3-2

Answer: Example 3-Practice 1, a = 10. Example 3-Practice 2, a = 45. Example 3-Practice 3, a = 400.

● Example 4-Practice 1 There is a circuit in which resistors are connected in parallel (10,
10 [Ω] in order from the top). Find the magnitude of the combined resistance
b [Ω]. (→ is the direction of current) Fig. 3-3

Example 4-Practice 2 There is a circuit in which resistors are connected in parallel (25, 25 [Ω] in order from the top). Find the magnitude of the combined resistance b [Ω]. (→ is the direction of current) Fig. 3-3

Example 4-Practice 3 There is a circuit in which resistors are connected in parallel (30, 70
[Ω] in order from the top). Find the magnitude of the combined resistance
b [Ω]. (→ is the direction of current) Fig. 3-3

Answer: Example 4-Practice 1, b = 5. Example 4-Practice 2, b = 12.5. Example
4-Practice 3, b = 21.

● Example 6-Practice 1 A current of 4 [A] is flowing through the resistor 5 [Ω]. Find the voltage drop a [V] that occurs across this resistor. Figure 4-2

Example 6-Practice 2 A current of 4 [A] is flowing through the resistor 5 [Ω]. Find the voltage
drop a [V] that occurs across this resistor. Figure 4-2

Example 6-Practice 3 A current of 4 [A] is flowing through the resistor 5 [Ω]. Find the voltage
drop a [V] that occurs across this resistor. Figure 4-2

Answer: Example 6-Exercise 1, a = 80. Example 6-Exercise 2, a = 75. Example 6-Exercise
3, a = 80.

● Example 7 There is a closed circuit consisting of one power supply and one resistor.
Answer the following questions. Figure 5-4

Exercise (1) Find the resistance Ω [Ω] when the power supply voltage is 20 [V] and the current is 0.5 [A].

Exercise (2) Obtain the current A [A] when the power supply voltage is 100 [V] and
the resistance is 400 [Ω].

Exercise (3) Obtain the power supply voltage V [V] when the current is 1.7 [A] and
the resistance is 300 [Ω].

Answer: Example 7-Practice @, 40 [Ω]. Exercise A, 0.25 [A]. Exercise B, 51 [V].

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