Electric charge (\( Q \)) is a fundamental concept in electrical engineering and physics. This article will guide you through calculating electric charge using current (\( I \)) and time (\( t \)). We will explore three relatable real-life examples to illustrate the calculations.
Formula to Determine Electric Charge
The electric charge (\( Q \)) can be determined from the current (\( I \)) and the time (\( t \)) the current flows using the formula:
\[ Q = I \cdot t \]
where:
- \( Q \) is the electric charge (in coulombs).
- \( I \) is the current (in amperes).
- \( t \) is the time (in seconds).
Example 1: Charging a Smartphone Battery
Scenario: You are charging your smartphone with a charger that provides a current of \( 2 \, \text{A} \). If you charge your phone for \( 1.5 \, \text{hours} \), how much electric charge is delivered to the battery?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 1.5 \, \text{hours} \times 3600 \, \text{seconds/hour} \]
\[ t = 5400 \, \text{seconds} \]
2. Given:
\[ I = 2 \, \text{A} \]
\[ t = 5400 \, \text{seconds} \]
3. Substitute Values into the Electric Charge Formula:
\[ Q = I \cdot t \]
\[ Q = 2 \cdot 5400 \]
4. Perform the Calculation:
\[ Q = 10800 \, \text{C} \]
Final Value
The electric charge delivered to the smartphone battery is:
\[ Q = 10800 \, \text{C} \]
Example 2: Electric Car Charging
Scenario: An electric car is charged with a current of \( 32 \, \text{A} \) for \( 5 \, \text{hours} \). How much electric charge is transferred to the car's battery?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 5 \, \text{hours} \times 3600 \, \text{seconds/hour} \]
\[ t = 18000 \, \text{seconds} \]
2. Given:
\[ I = 32 \, \text{A} \]
\[ t = 18000 \, \text{seconds} \]
3. Substitute Values into the Electric Charge Formula:
\[ Q = I \cdot t \]
\[ Q = 32 \cdot 18000 \]
4. Perform the Calculation:
\[ Q = 576000 \, \text{C} \]
Final Value
The electric charge transferred to the car's battery is:
\[ Q = 576000 \, \text{C} \]
Example 3: Running a Small Electric Heater
Scenario: A small electric heater operates with a current of \( 10 \, \text{A} \) for \( 2 \, \text{minutes} \). How much electric charge is used during this period?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 2 \, \text{minutes} \times 60 \, \text{seconds/minute} \]
\[ t = 120 \, \text{seconds} \]
2. Given:
\[ I = 10 \, \text{A} \]
\[ t = 120 \, \text{seconds} \]
3. Substitute Values into the Electric Charge Formula:
\[ Q = I \cdot t \]
\[ Q = 10 \cdot 120 \]
4. Perform the Calculation:
\[ Q = 1200 \, \text{C} \]
Final Value
The electric charge used by the heater is:
\[ Q = 1200 \, \text{C} \]
Summary
To find the electric charge (\( Q \)) given the current (\( I \)) and time (\( t \)), use the formula:
\[ Q = I \cdot t \]
In the examples provided:
1. Charging a smartphone with \( 2 \, \text{A} \) for \( 1.5 \, \text{hours} \) delivers \( 10800 \, \text{C} \).
2. Charging an electric car with \( 32 \, \text{A} \) for \( 5 \, \text{hours} \) transfers \( 576000 \, \text{C} \).
3. Running a heater with \( 10 \, \text{A} \) for \( 2 \, \text{minutes} \) uses \( 1200 \, \text{C} \).
These calculations show how to compute the electric charge in various everyday situations, essential for managing electrical devices and understanding energy consumption.
