To determine the time (\( t \)) when electric energy (\( E \)) and power (\( P \)) are known, use the formula:
\[ t = \dfrac{E}{P} \]
where:
- \( t \) is the time (in seconds, s),
- \( E \) is the electric energy (in joules, J),
- \( P \) is the power (in watts, W).
Example 1: Time for a Fan to Consume Energy
Scenario: A fan consumes \( 90000 \, \text{J} \) of energy at a power of \( 30 \, \text{W} \). How long does it run?
Calculation:
1. Given:
\[ E = 90000 \, \text{J} \]
\[ P = 30 \, \text{W} \]
2. Substitute into the Time Formula:
\[ t = \dfrac{E}{P} \]
\[ t = \dfrac{90000}{30} \]
3. Calculate:
\[ t = 3000 \, \text{s} \]
Final Value: The fan runs for \( 3000 \, \text{s} \) (50 minutes).
Example 2: Time for a TV to Use Energy
Scenario: A TV uses \( 1080000 \, \text{J} \) of energy at \( 150 \, \text{W} \). How much time does it take?
Calculation:
1. Given:
\[ E = 1080000 \, \text{J} \]
\[ P = 150 \, \text{W} \]
2. Substitute into the Time Formula:
\[ t = \dfrac{E}{P} \]
\[ t = \dfrac{1080000}{150} \]
3. Calculate:
\[ t = 7200 \, \text{s} \]
Final Value: The TV runs for \( 7200 \, \text{s} \) (2 hours).
Example 3: Time for a Smartphone to Drain Battery
Scenario: A smartphone consumes \( 18000 \, \text{J} \) of energy at a power of \( 5 \, \text{W} \). How long does it last?
Calculation:
1. Given:
\[ E = 18000 \, \text{J} \]
\[ P = 5 \, \text{W} \]
2. Substitute into the Time Formula:
\[ t = \dfrac{E}{P} \]
\[ t = \dfrac{18000}{5} \]
3. Calculate:
\[ t = 3600 \, \text{s} \]
Final Value: The smartphone lasts for \( 3600 \, \text{s} \) (1 hour).
Summary
To find the time (\( t \)), use the formula:
\[ t = \dfrac{E}{P} \]
In the examples provided:
1. Fan: \( 3000 \, \text{s} \) (50 minutes)
2. TV: \( 7200 \, \text{s} \) (2 hours)
3. Smartphone: \( 3600 \, \text{s} \) (1 hour)
