Power

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レッスンノート

Definition of Power

Power is the rate at which energy is transferred.
The unit of power is the Watt (W).
One Watt equals one Joule per second (1 W = 1 J/s).

The motor that lifts the same weight through the same height in less time has more power

Power Equation

The equation linking power, energy and time is: Power = Energy ÷ Time.
In symbols: P = E ÷ t.
Energy is measured in Joules (J), time in seconds (s).
Rearranged: Energy = Power × Time (E = P × t).

Example Calculations

Example 1: A 5 W torch used for 30 s transfers 150 J of energy (E = 5 × 30).
Example 2: A toaster using 20,000 J in 100 s has a power of 200 W (P = 20,000 ÷ 100).

Kilowatts and Conversion

Power can be given in kilowatts (kW); 1 kW = 1000 W.
To convert kW to W: multiply by 1000.
To convert W to kW: divide by 1000.

Worked Examples from Workbook

Q3: Lamp: 2400 J in 40 s → Power = 2400 ÷ 40 = 60 W.
Q4: Motor: 4000 J in 200 s → Power = 4000 ÷ 200 = 20 W.
Q5: Microwave: 900 W for 15 s → Energy = 900 × 15 = 13,500 J.
Q6: Radiator: 2000 W for 90 s → Energy = 2000 × 90 = 180,000 J.
Q9: Washing machine: 2.2 kW for 20 min → Convert: 2.2 kW = 2200 W; 20 min = 1200 s; Energy = 2200 × 1200 = 2,640,000 J.

Key Points to Remember

Always use consistent units: Joules, seconds, Watts.
For time given in minutes, convert to seconds (×60).
For power in kW, convert to W (×1000) before calculation.

A simple circuit to measure power: P = V × I (though not directly covered, the circuit illustrates energy transfer).

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練習問題

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1.What is the unit of power?
Easy
- AWatt (W)
- BJoule (J)
- CSecond (s)
- DKilowatt-hour (kWh)
2.Which equation correctly relates power (P), energy (E), and time (t)?
Easy
- AP = E × t
- BP = E ÷ t
- CP = t ÷ E
- DP = E + t
3.How many watts are in one kilowatt?
Easy
- A10 W
- B100 W
- C1000 W
- D1 000 000 W
4.A lamp uses 2400 J of energy in 40 s. What is its power?
Easy
- A60 W
- B96 000 W
- C0.0167 W
- D600 W
5.A microwave has a power of 900 W. How much energy does it use in 15 s?
Easy
- A60 J
- B13 500 J
- C900 J
- D135 J
6.An electric motor uses 4000 J of energy in 200 s. What is its power?
Easy
- A20 W
- B200 W
- C800 000 W
- D0.05 W
7.A radiator has a power of 2000 W. How much energy does it use in 90 s?
Easy
- A22.2 J
- B180 000 J
- C2000 J
- D22 222 J
8.A washing machine has a power of 2.2 kW. How much energy does it use in 20 minutes?
Medium
- A44 J
- B2640 J
- C2 640 000 J
- D44 000 J

もっと問題

9.Power is defined as the rate at which __________ is transferred.
Easy
- Aenergy
- Bforce
- Cmass
- Dcurrent
10.A device transfers 500 J of energy in 10 s. What is its power?
Easy
- A50 W
- B5000 W
- C0.02 W
- D5 W
11.Which of the following is equivalent to 0.5 kW?
Easy
- A5 W
- B50 W
- C500 W
- D5000 W
12.A kettle has a power of 2.5 kW. If it is used for 3 minutes, how much energy does it transfer?
Medium
- A7500 J
- B450 000 J
- C7500 kJ
- D450 J
13.A 1.5 kW heater is used for 2 hours. How much energy does it transfer?
Medium
- A3 kWh
- B3000 J
- C10800 J
- D10.8 MJ
14.A wind turbine generates 600 kJ of energy in 5 minutes. What is its average power output?
Medium
- A2000 W
- B120 W
- C200 W
- D2 kW
15.A pump lifts 2000 kg of water through a height of 10 m in 40 s. The gravitational field strength is 10 N/kg. What is the power output of the pump?
Hard
- A500 W
- B5000 W
- C5 kW
- D50 kW
16.Which of the following is a correct unit for power?
Easy
- AJoule
- BJoule per second
- CJoule second
- DWatt per second
17.A 60 W light bulb is left on for 5 hours. How much energy does it use in kilowatt-hours?
Medium
- A0.3 kWh
- B300 kWh
- C0.012 kWh
- D12 kWh
18.A student investigates how the power of a motor varies with the load it lifts. The motor lifts a mass of 1 kg through 2 m in 4 s. What is the power? (g = 10 N/kg)
Medium
- A5 W
- B10 W
- C20 W
- D40 W
19.A solar panel produces 50 W of power. How much energy does it generate in 8 hours?
Medium
- A400 J
- B400 Wh
- C1.44 MJ
- D14.4 kJ
20.A battery has a total energy storage of 10 000 J. It powers a device that draws 5 W. How long will the battery last?
Medium
- A2000 s
- B500 s
- C50 000 s
- D200 s
21.A 3 kW kettle is used for 2 minutes. How much energy does it use in joules?
Medium
- A6000 J
- B360 000 J
- C6000 kJ
- D360 kJ
22.A machine does 5000 J of useful work in 25 s, but wastes 3000 J as heat. What is its power input?
Medium
- A200 W
- B320 W
- C80 W
- D500 W
23.A student measures the power of a small electric motor by lifting a mass. The motor lifts a 0.5 kg mass through a height of 1.2 m in 3.0 s. The gravitational field strength is 10 N/kg. What is the power output of the motor?
Medium
- A2.0 W
- B6.0 W
- C20 W
- D60 W
24.In an experiment to determine the power of a kettle, a student measures the time to heat 1 kg of water from 20°C to 100°C. The specific heat capacity of water is 4200 J/(kg·°C). The kettle is rated at 2.5 kW. Assuming no heat loss, what is the minimum time required?
Hard
- A134 s
- B168 s
- C224 s
- D336 s
25.A student investigates how the power of a lamp changes with the p.d. across it. She measures the current and p.d. for different settings. Which equation should she use to calculate the power?
Easy
- AP = I / V
- BP = V × I
- CP = V / I
- DP = I² × V
26.A student uses a joulemeter to measure the energy transferred by a 60 W lamp over 2 minutes. The joulemeter reading increases from 0 J to 7200 J. What is the percentage error compared to the expected energy?
Medium
- A0%
- B5%
- C10%
- D20%
27.A 1.5 kW heater is used for 2 hours. How much energy does it transfer in kilowatt-hours?
Easy
- A0.75 kWh
- B1.5 kWh
- C3.0 kWh
- D4.5 kWh
28.A solar panel has an efficiency of 15% and receives 800 W/m² of solar power. Its area is 2 m². What is its electrical power output?
Medium
- A120 W
- B240 W
- C160 W
- D80 W
29.What is the definition of power?
Easy
- AThe total energy transferred
- BThe rate at which energy is transferred
- CThe force applied over a distance
- DThe time taken to do work
30.Which of the following is the correct symbol for power?
Easy
- AE
- BP
- Ct
- DW
31.The unit of power is the watt. Which of the following is equivalent to 1 watt?
Easy
- A1 joule per second
- B1 joule per minute
- C1 joule per hour
- D1 newton per second
32.A device transfers 600 J of energy in 30 s. What is its power?
Easy
- A20 W
- B18000 W
- C0.05 W
- D600 W
33.A 100 W lamp is switched on for 2 minutes. How much energy does it use?
Easy
- A200 J
- B12000 J
- C1200 J
- D50 J
34.A 2.5 kW kettle is used for 4 minutes. How much energy does it transfer in joules?
Medium
- A600000 J
- B10000 J
- C6000 J
- D600 J
35.A motor does 5000 J of work in 25 s. What is its power output?
Easy
- A200 W
- B125000 W
- C20 W
- D5000 W
36.A pump lifts 200 kg of water through a height of 10 m in 40 s. Gravitational field strength is 10 N/kg. What is the power output of the pump?
Medium
- A500 W
- B50 W
- C5000 W
- D2000 W
37.How many watts are there in 0.5 kW?
Easy
- A500 W
- B50 W
- C5000 W
- D0.0005 W
38.A battery stores 10 000 J of energy. It powers a device that draws 5 W. How long will the battery last?
Medium
- A2000 s
- B50000 s
- C200 s
- D20 s
39.The unit of power is the watt (W).
Easy
True or false?
40.A 2 kW heater operates for 300 s. How much energy does it transfer?
Medium
- A600 kJ
- B6000 J
- C150 J
- D0.0067 J
41.To convert from kilowatts to watts, you divide by 1000.
Easy
True or false?
42.A device transfers 500 J of energy in 25 s. What is its power?
Easy
- A20 W
- B12500 W
- C0.05 W
- D525 W
43.Match each quantity to its correct unit.
Easy
- Power
- Energy
- Time
- Watt (W)
- Joule (J)
- Second (s)
44.Arrange the following steps in the correct order to calculate the power of a device that uses 3000 J in 60 s.
Medium
- Write down the equation: P = E ÷ t
- Insert values: P = 3000 ÷ 60
- Calculate: P = 50 W
- Identify given: E = 3000 J, t = 60 s
45.Which of the following are correct statements about power? (Select all that apply)
Medium
- APower is the rate at which energy is transferred.
- BThe unit of power is the watt.
- CPower = Energy × Time
- D1 kW = 1000 W
- EPower is measured in joules.
46.To convert from kilowatts to watts, you multiply by 1000.
Easy
True or false?
47.A device transfers 5000 J of energy in 25 s, but wastes 3000 J as heat. What is the power input of the device?
Medium
- A200 W
- B80 W
- C120 W
- D320 W
48.A device that transfers 500 J of energy in 25 s has a power of 20 W.
Easy
True or false?
49.Complete the sentence.
Easy
Power is defined as the rate at which ____ is transferred.
50.Convert the following powers.
Easy
2.5 kW = ____ W
51.State the equation that links power, energy and time.
Easy
52.A washing machine has a power of 2.2 kW. Calculate how much energy it uses in 20 minutes. Give your answer in joules.
Medium
53.A microwave has a power of 900 W. Calculate how much energy it will use in a time of 15 s. Show your working.
Medium
54.A washing machine has a power of 2.2 kW. Calculate how much energy it uses in 20 minutes. Give your answer in joules.
Medium
- A2376000 J
- B3168000 J
- C2640000 J
- D2904000 J

復習ノート

## Power Power is the **rate at which energy is transferred**. The unit of power is the **watt (W)**. ### Key Equations - **Power = Energy ÷ Time** \( P = \frac{E}{t} \) - **Energy = Power × Time** \( E = P \times t \) Energy is measured in **joules (J)**, time in **seconds (s)**. ### Worked Examples 1. **Torch**: \( P = 5\,\text{W} \), \( t = 30\,\text{s} \) \( E = P \times t = 5 \times 30 = 150\,\text{J} \) 2. **Toaster**: \( E = 20\,000\,\text{J} \), \( t = 100\,\text{s} \) \( P = E \div t = 20\,000 \div 100 = 200\,\text{W} \) ### Kilowatts - **1 kW = 1000 W** - To convert **kW → W**: multiply by 1000 - To convert **W → kW**: divide by 1000 ### Tips for Calculations - Always write the equation first. - Substitute values with units. - Calculate and include units in answer. - For time in minutes, convert to seconds (×60). - For power in kW, convert to W (×1000). ### Quick Practice - Lamp: \( E = 2400\,\text{J}, t = 40\,\text{s} \) → \( P = 60\,\text{W} \) - Motor: \( E = 4000\,\text{J}, t = 200\,\text{s} \) → \( P = 20\,\text{W} \) - Microwave: \( P = 900\,\text{W}, t = 15\,\text{s} \) → \( E = 13\,500\,\text{J} \) - Radiator: \( P = 2000\,\text{W}, t = 90\,\text{s} \) → \( E = 180\,000\,\text{J} \)

Power: The rate at which energy is transferred. Measured in watts (W).
Watt (W): The unit of power. One watt equals one joule per second.
Energy: Measured in joules (J). The capacity to do work.
Kilowatt (kW): A unit of power equal to 1000 watts.
P = E ÷ t: Equation linking power (P) in watts, energy (E) in joules, and time (t) in seconds.
E = P × t: Rearranged equation to calculate energy from power and time.

フラッシュカード

What is power?

Power is the rate at which energy is transferred.

What is the unit of power?

The unit of power is the Watt (W).

Write the equation linking power, energy and time.

Power = Energy ÷ Time, or P = E ÷ t.

Write the equation linking energy, power and time.

Energy = Power × Time, or E = P × t.

What is the unit of energy?

The unit of energy is the Joule (J).

What is the unit of time in power calculations?

The unit of time is the second (s).

A torch has a power of 5 W and is used for 30 s. Calculate the energy used.

E = P × t = 5 W × 30 s = 150 J.

A toaster uses 20,000 J of energy in 100 s. Calculate its power.

P = E ÷ t = 20,000 J ÷ 100 s = 200 W.

How many watts are in one kilowatt?

One kilowatt (kW) equals 1000 watts (W).

Convert 2 kW to watts.

2 kW × 1000 = 2000 W.

Convert 500 W to kilowatts.

500 W ÷ 1000 = 0.5 kW.

A lamp uses 2400 J in 40 s. Calculate its power.

P = E ÷ t = 2400 J ÷ 40 s = 60 W.

An electric motor uses 4000 J in 200 s. Calculate its power.

P = E ÷ t = 4000 J ÷ 200 s = 20 W.

A microwave has a power of 900 W. Calculate energy used in 15 s.

E = P × t = 900 W × 15 s = 13,500 J.

An electric radiator has a power of 2000 W. Calculate energy used in 90 s.

E = P × t = 2000 W × 90 s = 180,000 J.

A washing machine has a power of 2.2 kW. Convert to watts.

2.2 kW × 1000 = 2200 W.

Convert 20 minutes to seconds.

20 minutes × 60 = 1200 seconds.

A washing machine has a power of 2.2 kW. Calculate energy used in 20 minutes.

First convert: 2.2 kW = 2200 W, 20 min = 1200 s. Then E = P × t = 2200 W × 1200 s = 2,640,000 J.

What is the formula to convert kilowatts to watts?

Multiply the number of kilowatts by 1000: kW × 1000 → W.

What is the formula to convert watts to kilowatts?

Divide the number of watts by 1000: W ÷ 1000 → kW.

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