Question

Given below are two statements :
Statement (I) : The commercial unit of energy is 1 kWh.
Statement (II) : 1 kWh = \(2.6 \times 10^6\) J
In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

To convert kWh to Joules instantly:
Remember that a watt is a joule per second, and there are 3,600 seconds in an hour.
Multiply \(1,000 \times 3,600\) to get \(3.6 \times 10^6\) Joules (or 3.6 Megajoules).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Energy is defined as the capacity to do work.
In the International System of Units (SI), the unit of energy is the Joule (J).
However, for commercial and billing purposes, larger units like the kilowatt-hour (kWh) are used to measure electricity consumption.
Key Formula or Approach:
To convert kilowatt-hours (kWh) to Joules (J), we use the relationships:
\[ 1 \text{ kW} = 1000 \text{ W} = 1000 \text{ J/s} \]
\[ 1 \text{ hour} = 3600 \text{ seconds} \]
\[ 1 \text{ kWh} = 1 \text{ kW} \times 1 \text{ hour} \]

Step 2: Detailed Explanation:
Let us evaluate both statements:
- Statement (I): "The commercial unit of energy is 1 kWh."
This is a correct statement. Electric utility companies bill consumers based on the number of "units" consumed, where 1 unit is defined as 1 kilowatt-hour (kWh).
- Statement (II): "1 kWh = \(2.6 \times 10^6\) J"
Let us calculate the exact conversion of 1 kWh to Joules:
\[ 1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} \]
\[ 1 \text{ kWh} = 1000 \frac{\text{J}}{\text{s}} \times 3600 \text{ s} \]
\[ 1 \text{ kWh} = 3,600,000 \text{ J} = 3.6 \times 10^6 \text{ J} \]
The value given in Statement (II) is \(2.6 \times 10^6\) J, which is mathematically incorrect.
Therefore, Statement (I) is true but Statement (II) is false.
This matches Option (C).

Step 3: Final Answer:
The correct option is (C).