To determine which value is equivalent to one kilowatt-hour, we first need to understand the units involved.
1. A kilowatt-hour (kWh) is a measure of energy. Specifically, it is the amount of energy consumed if a device uses one kilowatt (1000 watts) of power continuously for one hour.
2. Energy can be converted to various units, but one of the most common conversions is to joules. The relationship between power, time, and energy is given by:
[tex]\[
\text{Energy} = \text{Power} \times \text{Time}
\][/tex]
3. By definition,
[tex]\[
1 \text{ kilowatt-hour} = 1000 \text{ watts} \times 1 \text{ hour}
\][/tex]
4. To convert hours to seconds (since the standard unit of energy, the joule, uses seconds), we know:
[tex]\[
1 \text{ hour} = 3600 \text{ seconds}
\][/tex]
5. Substituting this into our equation, we get:
[tex]\[
1 \text{ kilowatt-hour} = 1000 \text{ watts} \times 3600 \text{ seconds}
\][/tex]
6. Multiplying these together, we find:
[tex]\[
1 \text{ kilowatt-hour} = 1000 \times 3600 \text{ joules}
\][/tex]
[tex]\[
1 \text{ kilowatt-hour} = 3,600,000 \text{ joules}
\][/tex]
Since [tex]\(3,600,000\)[/tex] is equivalent to [tex]\(3.6 \times 10^6\)[/tex] joules, we can match this result with the options provided.
Thus, the correct answer is:
B. [tex]$3.6 \times 10^6$[/tex] joules
