What does a label such as “100V 1000W” on an appliance mean? This unit deals with the amount of electrical energy.
Basic Knowledge
Electric power P is the amount of work done by electricity in one second, and its unit is the watt (W).Electric power P [W] = voltage V [V] × current I [A]
Substituting Ohm’s law gives the following derived formulas:
・P = I²R
・P = V² / R
Electrical energy W is the total amount of energy obtained by multiplying power by time, and its unit is the joule (J) or watt-hour (Wh).Electrical energy W [J] = electric power P [W] × time t [seconds]
Household electricity charges are usually calculated in kilowatt-hours (kWh). 1kWh = 1000W × 1 hour = 3,600,000J.
Electric power P (electrical energy per second. Unit: W (watt))
Electrical energy W (total amount of electrical energy. Unit: J (joule) or Wh )
Heat energy Q (thermal energy produced. Unit: J (joule))
Joule’s law (heat produced by current Q = I²Rt )
Electric power company (a business that generates, transmits, and distributes electricity)
Energy conservation (efforts to reduce energy consumption)
Further Exploration (Background and Significance)
When current flows through a resistor, it always produces heat (Joule heat). This is because collisions between electrons and atoms inside the resistor change kinetic energy into heat. Electric heaters, toasters, electric kettles, and hair dryers all use this principle.
Heat energy can be found using the following equation: Q = Pt = IVt = I²Rt
1Wh = 3600J, 1kWh = 3.6 × 10⁶ J.
Example: If a 1000W microwave oven is used for 5 minutes,
Electrical energy = 1000 × 300 seconds = 300000 J = 300 kJ = approximately 0.083 kWh
If the electricity rate is 30 yen/kWh, the cost is approximately 2.5 yen.
Most of the electricity consumed worldwide faces the problem of losses caused by resistance during transmission. Therefore, before electricity reaches homes, substations raise the voltage to high voltage (tens of thousands to hundreds of thousands of V) and reduce the current to limit the I²R loss (the reason for raising the voltage).
- Electric power P = VI [W]
- Derived formulas: P = I²R = V²/R
- Electrical energy W = Pt [J] or [Wh]
- 1 Wh = 3600 J
- 1 kWh = 3.6×10⁶ J
- The appliance label “100V 1000W” shows the voltage and power during use
- High voltage transmission reduces I²R losses
Points to Note (Easily Confused)
① Electric power (W) is electrical energy per second, while electrical energy (J or Wh) is the accumulated energy. They are different: one is an instantaneous amount and the other is a cumulative amount. ② Electrical energy W and heat energy Q have the same unit (J), and when all the energy is converted into heat in a resistor, W = Q. ③ Unit conversion: 1 Wh = 3600 J. ④ The “1000W” on an appliance label is its rated power, or the power consumed during full operation.
Practice
- What is the power consumption in W of a light bulb through which a current of 2A flows from a 100V power source?
- Find the electrical energy in J used by a 500W electric kettle operated for 10 minutes.
- What is the name of the law that expresses the heat produced when current flows through a resistor?