To find electric energy (\( E \)) when voltage (\( V \)) and electric charge (\( Q \)) are known, use the formula:
\[ E = V \cdot Q \]
where:
- \( E \) is the electric energy (in joules, J),
- \( V \) is the voltage (in volts, V),
- \( Q \) is the electric charge (in coulombs, C).
Example 1: Energy Stored in a Capacitor
Scenario: A capacitor is charged to a voltage of \( 5 \, \text{V} \) and holds a charge of \( 0.2 \, \text{C} \). What is the electric energy stored?
Calculation:
1. Given:
\[ V = 5 \, \text{V} \]
\[ Q = 0.2 \, \text{C} \]
2. Substitute into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 5 \cdot 0.2 \]
3. Calculate:
\[ E = 1 \, \text{J} \]
Final Value: The electric energy stored in the capacitor is \( 1 \, \text{J} \).
Example 2: Energy in a Battery
Scenario: A battery supplies a voltage of \( 12 \, \text{V} \) and delivers a charge of \( 1 \, \text{C} \). What is the energy delivered by the battery?
Calculation:
1. Given:
\[ V = 12 \, \text{V} \]
\[ Q = 1 \, \text{C} \]
2. Substitute into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 12 \cdot 1 \]
3. Calculate:
\[ E = 12 \, \text{J} \]
Final Value: The energy delivered by the battery is \( 12 \, \text{J} \).
Example 3: Energy Consumed by an Electronic Device
Scenario: An electronic device operates at a voltage of \( 9 \, \text{V} \) and uses \( 0.5 \, \text{C} \) of charge. What is the energy consumed?
Calculation:
1. Given:
\[ V = 9 \, \text{V} \]
\[ Q = 0.5 \, \text{C} \]
2. Substitute into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 9 \cdot 0.5 \]
3. Calculate:
\[ E = 4.5 \, \text{J} \]
Final Value: The energy consumed by the device is \( 4.5 \, \text{J} \).
Summary
To find the electric energy (\( E \)), use the formula:
\[ E = V \cdot Q \]
In the examples provided:
1. Capacitor: \( 1 \, \text{J} \)
2. Battery: \( 12 \, \text{J} \)
3. Electronic device: \( 4.5 \, \text{J} \)
