Electric capacitance is a key property of capacitors, representing their ability to store charge. Knowing how to calculate capacitance can be essential in designing and analyzing electronic circuits. This article explains how to find the electric capacitance (\( C \)) when the electric charge (\( Q \)) and voltage (\( V \)) are given, using the formula \( C = \dfrac{Q}{V} \). We’ll provide three relatable examples with calculations.
Formula to Determine Electric Capacitance
Electric capacitance (\( C \)) can be calculated using the formula:
\[ C = \dfrac{Q}{V} \]
where:
- \( C \) is the capacitance (in farads, F),
- \( Q \) is the charge (in coulombs, C),
- \( V \) is the voltage (in volts, V).
Example 1: Capacitance of a Camera Flash
Scenario: A camera flash stores a charge of \( 0.002 \, \text{C} \) at \( 300 \, \text{V} \). What is the capacitance of the flash capacitor?
Step-by-Step Calculation:
1. Given:
\[ Q = 0.002 \, \text{C} \]
\[ V = 300 \, \text{V} \]
2. Substitute Values into the Capacitance Formula:
\[ C = \dfrac{Q}{V} \]
\[ C = \dfrac{0.002}{300} \]
3. Perform the Calculation:
\[ C = 0.00000667 \, \text{F} \]
Final Value
The capacitance of the camera flash capacitor is:
\[ C = 0.00000667 \, \text{F} \]
or \( 6.67 \, \mu\text{F} \).
Example 2: Capacitance of a Laptop Battery Backup
Scenario: A laptop battery backup capacitor stores \( 0.005 \, \text{C} \) at \( 50 \, \text{V} \). Find the capacitance.
Step-by-Step Calculation:
1. Given:
\[ Q = 0.005 \, \text{C} \]
\[ V = 50 \, \text{V} \]
2. Substitute Values into the Capacitance Formula:
\[ C = \dfrac{Q}{V} \]
\[ C = \dfrac{0.005}{50} \]
3. Perform the Calculation:
\[ C = 0.0001 \, \text{F} \]
Final Value
The capacitance of the laptop battery backup capacitor is:
\[ C = 0.0001 \, \text{F} \]
or \( 100 \, \mu\text{F} \).
Example 3: Capacitance of a Smartphone Power Supply
Scenario: A smartphone power supply capacitor stores \( 0.0015 \, \text{C} \) at \( 12 \, \text{V} \). Calculate the capacitance.
Step-by-Step Calculation:
1. Given:
\[ Q = 0.0015 \, \text{C} \]
\[ V = 12 \, \text{V} \]
2. Substitute Values into the Capacitance Formula:
\[ C = \dfrac{Q}{V} \]
\[ C = \dfrac{0.0015}{12} \]
3. Perform the Calculation:
\[ C = 0.000125 \, \text{F} \]
Final Value
The capacitance of the smartphone power supply capacitor is:
\[ C = 0.000125 \, \text{F} \]
or \( 125 \, \mu\text{F} \).
Summary
To find the electric capacitance (\( C \)) given the charge (\( Q \)) and voltage (\( V \)), use the formula:
\[ C = \dfrac{Q}{V} \]
In the examples provided:
1. A camera flash storing \( 0.002 \, \text{C} \) at \( 300 \, \text{V} \) has a capacitance of \( 6.67 \, \mu\text{F} \).
2. A laptop battery backup capacitor storing \( 0.005 \, \text{C} \) at \( 50 \, \text{V} \) has a capacitance of \( 100 \, \mu\text{F} \).
3. A smartphone power supply capacitor storing \( 0.0015 \, \text{C} \) at \( 12 \, \text{V} \) has a capacitance of \( 125 \, \mu\text{F} \).
