Understanding how to find the electric charge using electric energy and voltage is essential in electronics and electrical engineering. The relationship between electric energy (E), voltage (V), and electric charge (Q) is given by the formula:
\[ E = V \cdot Q \]
Where:
- \( E \) is the electric 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 electric charge, we rearrange the formula:
\[ Q = \dfrac{E}{V} \]
Example 1: Charging a Laptop Battery
Question: A laptop battery stores 54,000 joules of energy and operates at 12 volts. How much electric charge does it hold?
Calculation:
Given:
- \( E = 54,000 \) J
- \( V = 12 \) V
Using the formula:
\[ Q = \dfrac{54,000}{12} = 4,500 \text{ coulombs} \]
Result: The laptop battery holds 4,500 coulombs of electric charge.
Example 2: Electric Car Charging Station
Question: An electric car charging station delivers 180,000 joules of energy to a car battery at a voltage of 240 volts. What is the electric charge transferred?
Calculation:
Given:
- \( E = 180,000 \) J
- \( V = 240 \) V
Using the formula:
\[ Q = \dfrac{180,000}{240} = 750 \text{ coulombs} \]
Result: The electric charge transferred is 750 coulombs.
Example 3: Power Bank for Smartphones
Question: A power bank stores 36,000 joules of energy and has an output voltage of 5 volts. How much electric charge can it deliver?
Calculation:
Given:
- \( E = 36,000 \) J
- \( V = 5 \) V
Using the formula:
\[ Q = \dfrac{36,000}{5} = 7,200 \text{ coulombs} \]
Result: The power bank can deliver 7,200 coulombs of electric charge.
By understanding and applying this formula, you can easily determine the electric charge in various practical scenarios, whether you're dealing with laptop batteries, electric car charging stations, or power banks for smartphones. This fundamental concept is crucial for designing and troubleshooting electrical systems efficiently.
