Question

1 kWh = _____.

• A. \(3.6 \times 10^5 \text{ J}\)
• B. \(3.6 \times 10^6 \text{ J}\)
• C. \(3.6 \times 10^7 \text{ J}\)
• D. \(3.63 \times 10^6 \text{ J}\)

Hint:

To convert kWh to Joules: 1. kWh = kilowatt \(\times\) hour. 2. Convert kilowatt to watt: \(1 \text{ kW} = 1000 \text{ W}\). 3. Convert hour to seconds: \(1 \text{ hour} = 3600 \text{ s}\). 4. Multiply these values: \(1 \text{ kWh} = (1000 \text{ W}) \times (3600 \text{ s})\) Since \(1 \text{ W} = 1 \text{ J/s}\), \(1 \text{ kWh} = (1000 \text{ J/s}) \times (3600 \text{ s})\) \(1 \text{ kWh} = 1000 \times 3600 \text{ J}\) \(1 \text{ kWh} = 3,600,000 \text{ J}\) 5. In scientific notation: \(3.6 \times 10^6 \text{ J}\). This is also known as 1 "unit" of electricity in billing.

Answer 1

The Correct Option is B

Concept: kWh (kilowatt-hour) is a unit of energy, commonly used for electrical energy consumption. The Joule (J) is the SI unit of energy. We need to convert 1 kWh to Joules. Energy = Power \(\times\) Time. The SI unit of power is Watt (W), where 1 Watt = 1 Joule per second (1 W = 1 J/s). Step 1: Break down 1 kWh into its components 1 kWh means:
Power = 1 kilowatt (kW)
Time = 1 hour (h) Step 2: Convert kilowatt to watts 1 kilowatt (kW) = 1000 watts (W). So, Power = 1000 W. Step 3: Convert hour to seconds 1 hour (h) = 60 minutes 1 minute = 60 seconds So, 1 hour = \(60 \times 60 \text{ seconds} = 3600 \text{ seconds (s)}\). Time = 3600 s. Step 4: Calculate the energy in Joules Energy = Power \(\times\) Time Substitute the values in SI units (Watts for power, seconds for time): Energy = \((1000 \text{ W}) \times (3600 \text{ s})\) Since 1 W = 1 J/s: Energy = \((1000 \text{ J/s}) \times (3600 \text{ s})\) The 's' (seconds) unit cancels out: Energy = \(1000 \times 3600 \text{ J}\) Energy = \(3,600,000 \text{ J}\) Step 5: Express the energy in scientific notation To write 3,600,000 in scientific notation: Move the decimal point 6 places to the left to get 3.6. So, \(3,600,000 = 3.6 \times 10^6\). Therefore, \(1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\). This matches option (2).