Electric charge is a fundamental property of capacitors, indicating the amount of electrical energy they store. This article explains how to find the electric charge (\( Q \)) when capacitance (\( C \)) and voltage (\( V \)) are known, using the formula \( Q = C \cdot V \). We’ll provide three practical examples to illustrate the calculations.
Formula to Determine Electric Charge
Electric charge (\( Q \)) can be calculated using the formula:
\[ Q = C \cdot V \]
where:
- \( Q \) is the charge (in coulombs, C),
- \( C \) is the capacitance (in farads, F),
- \( V \) is the voltage (in volts, V).
Example 1: Charge Stored in a Camera Flash Capacitor
Scenario: A camera flash capacitor has a capacitance of \( 100 \, \mu\text{F} \) (microfarads) and is charged to \( 300 \, \text{V} \). What is the stored charge?
Step-by-Step Calculation:
1. Given:
\[ C = 100 \, \mu\text{F} = 100 \times 10^{-6} \, \text{F} \]
\[ V = 300 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = C \cdot V \]
\[ Q = (100 \times 10^{-6}) \cdot 300 \]
3. Perform the Calculation:
\[ Q = 0.03 \, \text{C} \]
Final Value
The charge stored in the camera flash capacitor is:
\[ Q = 0.03 \, \text{C} \]
Example 2: Charge in a Car Battery Capacitor
Scenario: A car battery capacitor has a capacitance of \( 4700 \, \mu\text{F} \) and is charged to \( 12 \, \text{V} \). Calculate the stored charge.
Step-by-Step Calculation:
1. Given:
\[ C = 4700 \, \mu\text{F} = 4700 \times 10^{-6} \, \text{F} \]
\[ V = 12 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = C \cdot V \]
\[ Q = (4700 \times 10^{-6}) \cdot 12 \]
3. Perform the Calculation:
\[ Q = 0.0564 \, \text{C} \]
Final Value
The charge in the car battery capacitor is:
\[ Q = 0.0564 \, \text{C} \]
Example 3: Charge in a Power Supply Capacitor
Scenario: A power supply capacitor has a capacitance of \( 330 \, \mu\text{F} \) and a voltage of \( 24 \, \text{V} \). What is the stored charge?
Step-by-Step Calculation:
1. Given:
\[ C = 330 \, \mu\text{F} = 330 \times 10^{-6} \, \text{F} \]
\[ V = 24 \, \text{V} \]
2. Substitute Values into the Charge Formula:
\[ Q = C \cdot V \]
\[ Q = (330 \times 10^{-6}) \cdot 24 \]
3. Perform the Calculation:
\[ Q = 0.00792 \, \text{C} \]
Final Value
The charge in the power supply capacitor is:
\[ Q = 0.00792 \, \text{C} \]
Summary
To find the electric charge (\( Q \)) given the capacitance (\( C \)) and voltage (\( V \)), use the formula:
\[ Q = C \cdot V \]
In the examples provided:
1. A camera flash capacitor with \( 100 \, \mu\text{F} \) and \( 300 \, \text{V} \) stores \( 0.03 \, \text{C} \).
2. A car battery capacitor with \( 4700 \, \mu\text{F} \) and \( 12 \, \text{V} \) stores \( 0.0564 \, \text{C} \).
3. A power supply capacitor with \( 330 \, \mu\text{F} \) and \( 24 \, \text{V} \) stores \( 0.00792 \, \text{C} \).
