Understanding how to calculate voltage when given the electrical energy and charge is crucial in various fields, including electronics, engineering, and physics. The relationship between these quantities is governed by a simple yet powerful formula.
The Formula: \(E = V \cdot Q\)
The formula to find voltage using energy and charge is expressed as:
\[ E = V \cdot Q \]
Where:
- \(E\) is the electrical energy (measured in joules, J)
- \(V\) is the voltage (measured in volts, V)
- \(Q\) is the electric charge (measured in coulombs, C)
To find the voltage (\(V\)), we can rearrange the formula as follows:
\[ V = \dfrac{E}{Q} \]
Example 1: Charging a Mobile Phone Battery
Question: A mobile phone battery stores 9000 joules of energy and the total charge is 3000 coulombs. What is the voltage of the battery?
Calculation:
Given:
- \(E = 9000\) J
- \(Q = 3000\) C
Using the formula:
\[ V = \dfrac{E}{Q} = \dfrac{9000}{3000} = 3 \, \text{V} \]
Result: The voltage of the mobile phone battery is 3 volts.
Example 2: Electric Car Battery
Question: An electric car battery stores 1,200,000 joules of energy and the total charge is 4000 coulombs. What is the voltage of the car battery?
Calculation:
Given:
- \(E = 1,200,000\) J
- \(Q = 4000\) C
Using the formula:
\[ V = \dfrac{E}{Q} = \dfrac{1,200,000}{4000} = 300 \, \text{V} \]
Result: The voltage of the electric car battery is 300 volts.
Example 3: Capacitor in a Circuit
Question: A capacitor in an electronic circuit stores 150 joules of energy and has a charge of 50 coulombs. What is the voltage across the capacitor?
Calculation:
Given:
- \(E = 150\) J
- \(Q = 50\) C
Using the formula:
\[ V = \dfrac{E}{Q} = \dfrac{150}{50} = 3 \, \text{V} \]
Result: The voltage across the capacitor is 3 volts.
Conclusion
By using the formula \(E = V \cdot Q\), you can easily find the voltage when the electrical energy and charge are known. This relationship is essential for understanding and designing various electrical and electronic systems. Whether you are dealing with batteries, capacitors, or any other electrical components, knowing how to calculate voltage from energy and charge is a valuable skill.
