Understanding electric current is crucial in various real-life applications such as charging devices, operating electrical appliances, and managing power systems. This article explains how to calculate electric current (\( I \)) when electric charge (\( Q \)) and time (\( t \)) are given. We will explore three relatable examples to illustrate the calculations.
Formula to Determine Electric Current
Electric current (\( I \)) can be calculated from the electric charge (\( Q \)) and the time (\( t \)) using the formula:
\[ I = \dfrac{Q}{t} \]
where:
- \( I \) is the electric current (in amperes).
- \( Q \) is the electric charge (in coulombs).
- \( t \) is the time (in seconds).
Example 1: Determining the Charging Current for a Smartphone
Scenario: You know that \( 5400 \, \text{C} \) of charge is delivered to your smartphone in \( 3 \, \text{hours} \). What is the current provided by the charger?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 3 \, \text{hours} \times 3600 \, \text{seconds/hour} \]
\[ t = 10800 \, \text{seconds} \]
2. Given:
\[ Q = 5400 \, \text{C} \]
\[ t = 10800 \, \text{seconds} \]
3. Substitute Values into the Electric Current Formula:
\[ I = \dfrac{Q}{t} \]
\[ I = \dfrac{5400}{10800} \]
4. Perform the Calculation:
\[ I = 0.5 \, \text{A} \]
Final Value
The charging current for the smartphone is:
\[ I = 0.5 \, \text{A} \]
Example 2: Finding the Current for an Electric Car Charger
Scenario: An electric car receives \( 576000 \, \text{C} \) of charge over \( 6 \, \text{hours} \). What is the current supplied by the charger?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 6 \, \text{hours} \times 3600 \, \text{seconds/hour} \]
\[ t = 21600 \, \text{seconds} \]
2. Given:
\[ Q = 576000 \, \text{C} \]
\[ t = 21600 \, \text{seconds} \]
3. Substitute Values into the Electric Current Formula:
\[ I = \dfrac{Q}{t} \]
\[ I = \dfrac{576000}{21600} \]
4. Perform the Calculation:
\[ I = 26.67 \, \text{A} \]
Final Value
The charging current for the electric car is:
\[ I = 26.67 \, \text{A} \]
Example 3: Calculating the Current for a Household Appliance
Scenario: A household appliance uses \( 1200 \, \text{C} \) of charge in \( 10 \, \text{minutes} \). What is the operating current?
Step-by-Step Calculation:
1. Convert Time to Seconds:
\[ t = 10 \, \text{minutes} \times 60 \, \text{seconds/minute} \]
\[ t = 600 \, \text{seconds} \]
2. Given:
\[ Q = 1200 \, \text{C} \]
\[ t = 600 \, \text{seconds} \]
3. Substitute Values into the Electric Current Formula:
\[ I = \dfrac{Q}{t} \]
\[ I = \dfrac{1200}{600} \]
4. Perform the Calculation:
\[ I = 2 \, \text{A} \]
Final Value
The operating current for the household appliance is:
\[ I = 2 \, \text{A} \]
Summary
To find the electric current (\( I \)) given the electric charge (\( Q \)) and time (\( t \)), use the formula:
\[ I = \dfrac{Q}{t} \]
In the examples provided:
1. Charging a smartphone with \( 5400 \, \text{C} \) over \( 3 \, \text{hours} \) requires \( 0.5 \, \text{A} \).
2. Charging an electric car with \( 576000 \, \text{C} \) over \( 6 \, \text{hours} \) needs \( 26.67 \, \text{A} \).
3. A household appliance using \( 1200 \, \text{C} \) in \( 10 \, \text{minutes} \) operates at \( 2 \, \text{A} \).
These calculations show how to compute the electric current in various practical situations, essential for evaluating power requirements and ensuring safe and efficient electrical operation.
