Determining electric charge from energy and voltage is crucial for understanding battery capacity, energy consumption, and the operation of electrical devices. This article will guide you on how to find the electric charge (\( Q \)) when energy (\( E \)) and voltage (\( V \)) are given. We'll provide three relatable examples to illustrate these calculations.
Formula to Determine Electric Charge
Electric charge (\( Q \)) can be calculated from energy (\( E \)) and voltage (\( V \)) using the formula:
\[ Q = \dfrac{E}{V} \]
where:
- \( Q \) is the electric charge (in coulombs).
- \( E \) is the energy (in joules).
- \( V \) is the voltage (in volts).
Example 1: Calculating Charge for a Smartphone Battery
Scenario: You have a smartphone battery that stores \( 18000 \, \text{J} \) of energy at a voltage of \( 3.7 \, \text{V} \). How much charge does the battery hold?
Step-by-Step Calculation:
1. Given:
\[ E = 18000 \, \text{J} \]
\[ V = 3.7 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{18000}{3.7} \]
3. Perform the Calculation:
\[ Q \approx 4864.86 \, \text{C} \]
Final Value
The charge stored in the smartphone battery is:
\[ Q \approx 4864.86 \, \text{C} \]
Example 2: Determining Charge for an Electric Car Battery
Scenario: An electric car battery stores \( 8640000 \, \text{J} \) of energy at a voltage of \( 400 \, \text{V} \). How much charge is stored in the battery?
Step-by-Step Calculation:
1. Given:
\[ E = 8640000 \, \text{J} \]
\[ V = 400 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{8640000}{400} \]
3. Perform the Calculation:
\[ Q = 21600 \, \text{C} \]
Final Value
The charge stored in the electric car battery is:
\[ Q = 21600 \, \text{C} \]
Example 3: Calculating Charge for a Household Appliance
Scenario: A household appliance uses \( 3000 \, \text{J} \) of energy at a voltage of \( 120 \, \text{V} \). How much charge does it consume?
Step-by-Step Calculation:
1. Given:
\[ E = 3000 \, \text{J} \]
\[ V = 120 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = \dfrac{E}{V} \]
\[ Q = \dfrac{3000}{120} \]
3. Perform the Calculation:
\[ Q = 25 \, \text{C} \]
Final Value
The charge consumed by the household appliance is:
\[ Q = 25 \, \text{C} \]
Summary
To find the electric charge (\( Q \)) given the energy (\( E \)) and voltage (\( V \)), use the formula:
\[ Q = \dfrac{E}{V} \]
In the examples provided:
1. A smartphone battery with \( 18000 \, \text{J} \) of energy and \( 3.7 \, \text{V} \) voltage holds approximately \( 4864.86 \, \text{C} \).
2. An electric car battery with \( 8640000 \, \text{J} \) of energy and \( 400 \, \text{V} \) voltage holds \( 21600 \, \text{C} \).
3. A household appliance using \( 3000 \, \text{J} \) of energy at \( 120 \, \text{V} \) consumes \( 25 \, \text{C} \).
These calculations help in understanding the charge requirements and efficiency of different electrical devices, making it easier to estimate battery life, power consumption, and operational efficiency.
