To find electric potential (\( V \)) when electric energy (\( E \)) and electric charge (\( Q \)) are known, use the formula:
\[ V = \dfrac{E}{Q} \]
where:
- \( V \) is the voltage (in volts, V),
- \( E \) is the electric energy (in joules, J),
- \( Q \) is the electric charge (in coulombs, C).
Example 1: Potential Across a Capacitor
Scenario: A capacitor stores \( 20 \, \text{J} \) of energy with a charge of \( 4 \, \text{C} \). What is the electric potential?
Calculation:
1. Given:
\[ E = 20 \, \text{J} \]
\[ Q = 4 \, \text{C} \]
2. Substitute into the Potential Formula:
\[ V = \dfrac{E}{Q} \]
\[ V = \dfrac{20}{4} \]
3. Calculate:
\[ V = 5 \, \text{V} \]
Final Value: The electric potential is \( 5 \, \text{V} \).
Example 2: Potential in a Battery
Scenario: A battery delivers \( 48 \, \text{J} \) of energy with a charge of \( 6 \, \text{C} \). What is the voltage?
Calculation:
1. Given:
\[ E = 48 \, \text{J} \]
\[ Q = 6 \, \text{C} \]
2. Substitute into the Potential Formula:
\[ V = \dfrac{E}{Q} \]
\[ V = \dfrac{48}{6} \]
3. Calculate:
\[ V = 8 \, \text{V} \]
Final Value: The voltage is \( 8 \, \text{V} \).
Example 3: Potential of an Appliance
Scenario: An appliance uses \( 36 \, \text{J} \) of energy with a charge of \( 3 \, \text{C} \). What is the potential?
Calculation:
1. Given:
\[ E = 36 \, \text{J} \]
\[ Q = 3 \, \text{C} \]
2. Substitute into the Potential Formula:
\[ V = \dfrac{E}{Q} \]
\[ V = \dfrac{36}{3} \]
3. Calculate:
\[ V = 12 \, \text{V} \]
Final Value: The electric potential is \( 12 \, \text{V} \).
Summary
To find the electric potential (\( V \)), use the formula:
\[ V = \dfrac{E}{Q} \]
In the examples provided:
1. Capacitor: \( 5 \, \text{V} \)
2. Battery: \( 8 \, \text{V} \)
3. Appliance: \( 12 \, \text{V} \)
