Determining the time required for a specific amount of electric energy consumption given the power is important for managing energy usage. The relationship between these quantities can be calculated using a specific formula, which we will explore with practical examples.
The Formula: \( P = \dfrac{E}{t} \)
To find the time, we rearrange the formula as follows:
\[ t = \dfrac{E}{P} \]
Where:
- \( P \) is the electric power (measured in watts, W)
- \( E \) is the electric energy (measured in joules, J)
- \( t \) is the time (measured in seconds, s)
Example 1: Operating Time of a Television
Question: A television consumes 540,000 joules of energy and operates at 150 watts. How long can the television run?
Calculation:
Given:
- \( E = 540,000 \) J
- \( P = 150 \) W
Using the formula:
\[ t = \dfrac{E}{P} = \dfrac{540,000}{150} = 3600 \, \text{s} \]
Result: The television can run for 3600 seconds (or 1 hour).
Example 2: Charging Time of a Laptop
Question: A laptop battery stores 180,000 joules of energy and charges at a rate of 60 watts. How long does it take to fully charge the battery?
Calculation:
Given:
- \( E = 180,000 \) J
- \( P = 60 \) W
Using the formula:
\[ t = \dfrac{E}{P} = \dfrac{180,000}{60} = 3000 \, \text{s} \]
Result: It takes 3000 seconds (or 50 minutes) to fully charge the laptop battery.
Example 3: Running Time of a Fan
Question: A fan uses 36,000 joules of energy and operates at 100 watts. How long will the fan run?
Calculation:
Given:
- \( E = 36,000 \) J
- \( P = 100 \) W
Using the formula:
\[ t = \dfrac{E}{P} = \dfrac{36,000}{100} = 360 \, \text{s} \]
Result: The fan will run for 360 seconds (or 6 minutes).
