Determining energy in electrical systems is essential for understanding battery capacity, power consumption, and the overall performance of electrical devices. This article will guide you on how to find the energy (\( E \)) when voltage (\( V \)) and electric charge (\( Q \)) are given. We will provide three relatable examples to illustrate these calculations.
Formula to Determine Energy
Energy (\( E \)) can be calculated from voltage (\( V \)) and electric charge (\( Q \)) using the formula:
\[ E = V \cdot Q \]
where:
- \( E \) is the energy (in joules).
- \( V \) is the voltage (in volts).
- \( Q \) is the electric charge (in coulombs).
Example 1: Calculating Energy for a Smartphone Battery
Scenario: You have a smartphone battery that provides \( 3.7 \, \text{V} \) and has a charge of \( 5000 \, \text{C} \). How much energy does the battery store?
Step-by-Step Calculation:
1. Given:
\[ V = 3.7 \, \text{V} \]
\[ Q = 5000 \, \text{C} \]
2. Substitute Values into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 3.7 \cdot 5000 \]
3. Perform the Calculation:
\[ E = 18500 \, \text{J} \]
Final Value
The energy stored in the smartphone battery is:
\[ E = 18500 \, \text{J} \]
Example 2: Determining Energy for an Electric Car Battery
Scenario: An electric car battery operates at \( 400 \, \text{V} \) and has a charge of \( 15000 \, \text{C} \). How much energy is stored in the battery?
Step-by-Step Calculation:
1. Given:
\[ V = 400 \, \text{V} \]
\[ Q = 15000 \, \text{C} \]
2. Substitute Values into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 400 \cdot 15000 \]
3. Perform the Calculation:
\[ E = 6000000 \, \text{J} \]
Final Value
The energy stored in the electric car battery is:
\[ E = 6000000 \, \text{J} \]
Example 3: Calculating Energy for a Household Appliance
Scenario: A household appliance operates at \( 120 \, \text{V} \) and uses a charge of \( 50 \, \text{C} \). How much energy does it consume?
Step-by-Step Calculation:
1. Given:
\[ V = 120 \, \text{V} \]
\[ Q = 50 \, \text{C} \]
2. Substitute Values into the Energy Formula:
\[ E = V \cdot Q \]
\[ E = 120 \cdot 50 \]
3. Perform the Calculation:
\[ E = 6000 \, \text{J} \]
Final Value
The energy consumed by the household appliance is:
\[ E = 6000 \, \text{J} \]
Summary
To find the energy (\( E \)) given the voltage (\( V \)) and electric charge (\( Q \)), use the formula:
\[ E = V \cdot Q \]
In the examples provided:
1. A smartphone battery with \( 3.7 \, \text{V} \) and \( 5000 \, \text{C} \) charge stores \( 18500 \, \text{J} \) of energy.
2. An electric car battery with \( 400 \, \text{V} \) and \( 15000 \, \text{C} \) charge stores \( 6000000 \, \text{J} \) of energy.
3. A household appliance operating at \( 120 \, \text{V} \) and using \( 50 \, \text{C} \) of charge consumes \( 6000 \, \text{J} \) of energy.
These calculations help in understanding the energy requirements and efficiency of various electrical devices, allowing for better energy management and cost estimation.
