To determine electric power (\( P \)) when energy (\( E \)) and time (\( t \)) are known, use the formula:
\[ P = \dfrac{E}{t} \]
where:
- \( P \) is the power (in watts, W),
- \( E \) is the electric energy (in joules, J),
- \( t \) is the time (in seconds, s).
Example 1: Power of a Computer
Scenario: A computer consumes \( 216000 \, \text{J} \) of energy in 1 hour. What is its power consumption?
Calculation:
1. Convert time to seconds:
\[ t = 1 \, \text{hour} \times 3600 \, \text{s/hour} = 3600 \, \text{s} \]
2. Given:
\[ E = 216000 \, \text{J} \]
\[ t = 3600 \, \text{s} \]
3. Substitute into the Power Formula:
\[ P = \dfrac{E}{t} \]
\[ P = \dfrac{216000}{3600} \]
4. Calculate:
\[ P = 60 \, \text{W} \]
Final Value: The power consumption of the computer is \( 60 \, \text{W} \).
Example 2: Power of a Microwave
Scenario: A microwave oven uses \( 540000 \, \text{J} \) of energy over 5 minutes. What is its power?
Calculation:
1. Convert time to seconds:
\[ t = 5 \, \text{minutes} \times 60 \, \text{s/minute} = 300 \, \text{s} \]
2. Given:
\[ E = 540000 \, \text{J} \]
\[ t = 300 \, \text{s} \]
3. Substitute into the Power Formula:
\[ P = \dfrac{E}{t} \]
\[ P = \dfrac{540000}{300} \]
4. Calculate:
\[ P = 1800 \, \text{W} \]
Final Value: The power of the microwave is \( 1800 \, \text{W} \).
Example 3: Power of an Electric Kettle
Scenario: An electric kettle consumes \( 1800000 \, \text{J} \) of energy in 10 minutes. What is its power rating?
Calculation:
1. Convert time to seconds:
\[ t = 10 \, \text{minutes} \times 60 \, \text{s/minute} = 600 \, \text{s} \]
2. Given:
\[ E = 1800000 \, \text{J} \]
\[ t = 600 \, \text{s} \]
3. Substitute into the Power Formula:
\[ P = \dfrac{E}{t} \]
\[ P = \dfrac{1800000}{600} \]
4. Calculate:
\[ P = 3000 \, \text{W} \]
Final Value: The power rating of the electric kettle is \( 3000 \, \text{W} \).
Summary
To find the electric power (\( P \)), use the formula:
\[ P = \dfrac{E}{t} \]
In the examples provided:
1. Computer: \( 60 \, \text{W} \)
2. Microwave: \( 1800 \, \text{W} \)
3. Electric kettle: \( 3000 \, \text{W} \)
