Question

question 11 (1 point)
a kilowatt - hour is equivalent to
1000 w.
3600 s.
3,600,000 j/s.
3,600,000 j.

Explanation:

Step1: Recall the definitions of power and energy

Power \( P \) is defined as energy \( E \) per unit time \( t \), so \( P=\frac{E}{t} \), which can be rearranged to \( E = P\times t \). The unit of power is watt (W), where \( 1\space W = 1\space J/s \), and 1 kilowatt (kW) is \( 1000\space W \). A kilowatt - hour (kWh) is the energy consumed when a power of 1 kilowatt is used for 1 hour.

Step2: Convert the units

First, convert 1 kilowatt to watts: \( 1\space kW=1000\space W = 1000\space J/s \) (since \( 1\space W = 1\space J/s \)).
Then, convert 1 hour to seconds. We know that 1 hour \( = 3600\space s \).
Now, calculate the energy in joules using \( E=P\times t \). Substitute \( P = 1000\space J/s \) and \( t = 3600\space s \) into the formula:
\( E=1000\space J/s\times3600\space s=3600000\space J \)

Let's analyze the other options:

• Option 1: \( 1000\space W \) is the definition of 1 kilowatt, not a kilowatt - hour (which is a unit of energy, not power).
• Option 2: \( 3600\space s \) is the number of seconds in an hour, not related to the energy equivalent of a kilowatt - hour.
• Option 3: \( 3600000\space J/s \) would be a power unit (since \( J/s = W \)), but a kilowatt - hour is an energy unit, so this is incorrect.

Answer:

3,600,000 J (the last option)