Understanding how to calculate time given electric charge and current is essential in everyday situations like estimating battery life, charging times, and power usage. This article explains how to determine the time (\( t \)) when electric charge (\( Q \)) and electric current (\( I \)) are given. We will explore three relatable examples to illustrate these calculations.
Formula to Determine Time
Time (\( t \)) can be calculated from the electric charge (\( Q \)) and electric current (\( I \)) using the formula:
\[ t = \dfrac{Q}{I} \]
where:
- \( t \) is the time (in seconds).
- \( Q \) is the electric charge (in coulombs).
- \( I \) is the electric current (in amperes).
Example 1: Determining the Charging Time for a Smartphone
Scenario: Your smartphone battery requires \( 5400 \, \text{C} \) of charge to fully charge. If the charger provides a current of \( 1.5 \, \text{A} \), how long will it take to fully charge the battery?
Step-by-Step Calculation:
1. Given:
\[ Q = 5400 \, \text{C} \]
\[ I = 1.5 \, \text{A} \]
2. Substitute Values into the Time Formula:
\[ t = \dfrac{Q}{I} \]
\[ t = \dfrac{5400}{1.5} \]
3. Perform the Calculation:
\[ t = 3600 \, \text{seconds} \]
4. Convert Time to Hours:
\[ t = \dfrac{3600}{3600} \]
\[ t = 1 \, \text{hour} \]
Final Value
The time to fully charge the smartphone is:
\[ t = 1 \, \text{hour} \]
Example 2: Finding the Charging Time for an Electric Car
Scenario: An electric car needs \( 720000 \, \text{C} \) of charge. If the charger provides \( 20 \, \text{A} \) of current, how long will it take to charge the car?
Step-by-Step Calculation:
1. Given:
\[ Q = 720000 \, \text{C} \]
\[ I = 20 \, \text{A} \]
2. Substitute Values into the Time Formula:
\[ t = \dfrac{Q}{I} \]
\[ t = \dfrac{720000}{20} \]
3. Perform the Calculation:
\[ t = 36000 \, \text{seconds} \]
4. Convert Time to Hours:
\[ t = \dfrac{36000}{3600} \]
\[ t = 10 \, \text{hours} \]
Final Value
The time to charge the electric car is:
\[ t = 10 \, \text{hours} \]
Example 3: Calculating the Usage Time for a Household Appliance
Scenario: A household appliance draws \( 5 \, \text{A} \) of current. If it uses \( 3000 \, \text{C} \) of charge, how long can it operate?
Step-by-Step Calculation:
1. Given:
\[ Q = 3000 \, \text{C} \]
\[ I = 5 \, \text{A} \]
2. Substitute Values into the Time Formula:
\[ t = \dfrac{Q}{I} \]
\[ t = \dfrac{3000}{5} \]
3. Perform the Calculation:
\[ t = 600 \, \text{seconds} \]
4. Convert Time to Minutes:
\[ t = \dfrac{600}{60} \]
\[ t = 10 \, \text{minutes} \]
Final Value
The appliance can operate for:
\[ t = 10 \, \text{minutes} \]
Summary
To find the time (\( t \)) given the electric charge (\( Q \)) and electric current (\( I \)), use the formula:
\[ t = \dfrac{Q}{I} \]
In the examples provided:
1. Charging a smartphone with \( 5400 \, \text{C} \) using \( 1.5 \, \text{A} \) takes \( 1 \, \text{hour} \).
2. Charging an electric car with \( 720000 \, \text{C} \) using \( 20 \, \text{A} \) takes \( 10 \, \text{hours} \).
3. A household appliance drawing \( 5 \, \text{A} \) and using \( 3000 \, \text{C} \) operates for \( 10 \, \text{minutes} \).
These calculations are practical for estimating how long devices and appliances will function based on their power requirements, ensuring efficient use of electrical energy.
