To determine the electric energy (\( E \)) consumed using power (\( P \)) and time (\( t \)), use the formula:
\[ E = P \cdot t \]
where:
- \( E \) is the electric energy (in joules, J),
- \( P \) is the power (in watts, W),
- \( t \) is the time (in seconds, s).
Example 1: Energy Consumed by a Light Bulb
Scenario: A 60-watt light bulb is used for 2 hours. How much energy does it consume?
Calculation:
1. Convert time to seconds:
\[ t = 2 \, \text{hours} \times 3600 \, \text{s/hour} = 7200 \, \text{s} \]
2. Given:
\[ P = 60 \, \text{W} \]
\[ t = 7200 \, \text{s} \]
3. Substitute into the Energy Formula:
\[ E = P \cdot t \]
\[ E = 60 \cdot 7200 \]
4. Calculate:
\[ E = 432000 \, \text{J} \]
Final Value: The energy consumed by the light bulb is \( 432000 \, \text{J} \) (432 kJ).
Example 2: Energy Used by a Heater
Scenario: An electric heater operates at 1500 watts for 3 hours. What is the total energy used?
Calculation:
1. Convert time to seconds:
\[ t = 3 \, \text{hours} \times 3600 \, \text{s/hour} = 10800 \, \text{s} \]
2. Given:
\[ P = 1500 \, \text{W} \]
\[ t = 10800 \, \text{s} \]
3. Substitute into the Energy Formula:
\[ E = P \cdot t \]
\[ E = 1500 \cdot 10800 \]
4. Calculate:
\[ E = 16200000 \, \text{J} \]
Final Value: The energy used by the heater is \( 16200000 \, \text{J} \) (16.2 MJ).
Example 3: Energy Consumed by a Washing Machine
Scenario: A washing machine runs at 500 watts for 45 minutes. How much energy is consumed?
Calculation:
1. Convert time to seconds:
\[ t = 45 \, \text{minutes} \times 60 \, \text{s/minute} = 2700 \, \text{s} \]
2. Given:
\[ P = 500 \, \text{W} \]
\[ t = 2700 \, \text{s} \]
3. Substitute into the Energy Formula:
\[ E = P \cdot t \]
\[ E = 500 \cdot 2700 \]
4. Calculate:
\[ E = 1350000 \, \text{J} \]
Final Value: The energy consumed by the washing machine is \( 1350000 \, \text{J} \) (1.35 MJ).
Summary
To find the electric energy (\( E \)), use the formula:
\[ E = P \cdot t \]
In the examples provided:
1. Light bulb: \( 432000 \, \text{J} \)
2. Heater: \( 16200000 \, \text{J} \)
3. Washing machine: \( 1350000 \, \text{J} \)
