Many products around us, such as household appliances and industrial products, operate using electricity.

These products achieve their functions by converting electrical energy into various other forms of energy, such as heat, light, and motion.

For example, a heater converts electrical energy into thermal energy, and an electric motor converts it into kinetic energy. A microwave oven uses electrical energy to generate microwaves, which heat food.

This section covers electric power, electric energy, and Joule’s law, which are related to electrical energy.

1.12.1 Electric Power and Electric Energy

As shown in Figure 1.12-1, when a current I flows through a load to which a voltage V is applied, electrical energy is consumed in the load.

Figure 1.12-1 Electric Power and Electric Energy

The electrical energy consumed or supplied per unit time is called electric power. Its unit is the watt (unit symbol: W), and its quantity symbol is P.

Electric power P [W] is obtained from the following equation.

The total amount of electrical energy when this power is used for a certain period of time is called electric energy. Its unit is the watt-second (W·s), and its quantity symbol is W.

That is, the electric energy W [W·s] when electric power P [W] is used for t seconds is obtained from the following equation.

The relationship between electric power and electric energy is easy to understand by comparing it with the relationship between speed, time, and distance traveled.
The distance traveled is determined by the speed and the time.

Distance traveled [m] = speed v [m/s] × time t [s]

Similarly, electric energy is determined by the electric power and the time it is used.

Electric energy [W·s] = electric power P [W] × time t [s]

In other words, if electric power P is compared to “speed,” electric energy W corresponds to “distance traveled.”
Even at the same power, the longer the time of use, the greater the electric energy.

1.12.2 Joule’s Law

The relationship between electrical energy and thermal energy can be felt in everyday life.

For example, a light bulb becomes hot when it is lit, a smartphone becomes warm while charging, and a computer generates heat inside when it is used.

In this way, heat is generated in many situations where electricity is used.

When electrons move through a conductor, they repeatedly collide with atoms and other particles.
In this process, part of the electrical energy is converted into thermal energy.

The amount of thermal energy generated by a current flowing through a resistor is called the quantity of heat. Its quantity symbol is H, and its unit is the joule (unit symbol: J).

In Figure 1.12-1, the quantity of heat H [J] generated when a current I [A] flows through a resistor R [Ω] for t seconds is expressed by the following equation.

This relationship was established through experiments by the British physicist James Prescott Joule.

The relationship in which the quantity of heat generated when a current flows through a resistor is proportional to the resistance R, the square of the current I, and the time t is called Joule’s law, and the heat generated is called Joule heat.

From Eq. (1.12-2) and Eq. (1.12-3), the following relationship is obtained.

In other words, the electrical energy consumed in a resistor is equal to the thermal energy generated by the resistor.

Since 1 J is equal to the energy when 1 W of power is used for 1 second, the following holds.

Therefore, the units of electric energy can be converted as follows.

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References

• Denki Kiso (Jo) [Fundamentals of Electricity, Vol. 1], Corona Publishing, Toshio Utsunomiya, Hiroshi Takahashi, Isao Izumi

*This article was compiled based on the author’s understanding, with reference to the above literature.