To find electric charge (\( Q \)) when voltage (\( V \)) and electric energy (\( E \)) are known, use the formula:
\[ Q = \dfrac{E}{V} \]
where:
- \( Q \) is the electric charge (in coulombs, C),
- \( E \) is the electric energy (in joules, J),
- \( V \) is the voltage (in volts, V).
Example 1: Charge in a Capacitor
Scenario: A capacitor stores \( 10 \, \text{J} \) of energy at a voltage of \( 5 \, \text{V} \). What is the electric charge?
Calculation:
1. Given:
\[ E = 10 \, \text{J} \]
\[ V = 5 \, \text{V} \]
2. Substitute into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{10}{5} \]
3. Calculate:
\[ Q = 2 \, \text{C} \]
Final Value: The electric charge is \( 2 \, \text{C} \).
Example 2: Charge in a Battery
Scenario: A battery delivers \( 24 \, \text{J} \) of energy at a voltage of \( 12 \, \text{V} \). What is the charge delivered?
Calculation:
1. Given:
\[ E = 24 \, \text{J} \]
\[ V = 12 \, \text{V} \]
2. Substitute into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{24}{12} \]
3. Calculate:
\[ Q = 2 \, \text{C} \]
Final Value: The charge delivered is \( 2 \, \text{C} \).
Example 3: Charge Used by an Appliance
Scenario: An appliance consumes \( 15 \, \text{J} \) of energy at a voltage of \( 3 \, \text{V} \). What is the charge used?
Calculation:
1. Given:
\[ E = 15 \, \text{J} \]
\[ V = 3 \, \text{V} \]
2. Substitute into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{15}{3} \]
3. Calculate:
\[ Q = 5 \, \text{C} \]
Final Value: The charge used by the appliance is \( 5 \, \text{C} \).
Summary
To find the electric charge (\( Q \)), use the formula:
\[ Q = \dfrac{E}{V} \]
In the examples provided:
1. Capacitor: \( 2 \, \text{C} \)
2. Battery: \( 2 \, \text{C} \)
3. Appliance: \( 5 \, \text{C} \)
