Reading Time: 2 minutes
Capacitors: Understanding Capacitance and Energy Storage in A-Level Science
What Is a Capacitor?
A capacitor is an electronic component that stores electrical energy in an electric field.
Capacitance and Its Formula
Capacitance (C)
Capacitance measures the ability of a capacitor to store charge per unit voltage:
![\[ C = \frac{Q}{V} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-17f8e9307332f62a728e632ed27042ed_l3.png "Rendered by QuickLaTeX.com")
Where:
: Capacitance (F, Farads)
: Charge (C, Coulombs)- : Voltage (V, Volts)
: Capacitance (F, Farads)
: Charge (C, Coulombs)
: Voltage (V, Volts)Energy Stored in a Capacitor
The energy (
) stored is given by:
![\[ E = \frac{1}{2}CV^2 \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-642188b998761dd3fcc79a0ebdfb9781_l3.png "Rendered by QuickLaTeX.com")
Example: A 
capacitor is charged to 
. Find the energy stored.
- Use the formula:
![\[ E = \frac{1}{2} \times 100 \times 10^{-6} \times 10^2 = 0.05 \, \text{J} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNzEiIGhlaWdodD0iMzYiIHZpZXdCb3g9IjAgMCAyNzEgMzYiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
![\[ E = \frac{1}{2} \times 100 \times 10^{-6} \times 10^2 = 0.05 \, \text{J} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-60915decd9198edd07c1d4542fabbdb8_l3.png "Rendered by QuickLaTeX.com")
Capacitor Configurations
Series Configuration
Capacitance decreases:
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-4e29a23468afcc94c37b23c63d014a0f_l3.png "Rendered by QuickLaTeX.com")
Parallel Configuration
Capacitance increases:
![\[ C_{\text{total}} = C_1 + C_2 + \dots \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-9b016f9030797c37acdad5c20a9806df_l3.png "Rendered by QuickLaTeX.com")
Applications of Capacitors
Energy Storage
Used in camera flashes and uninterruptible power supplies (UPS).
Signal Processing
Capacitors filter signals in audio equipment.
Electronics
Essential in timing circuits and oscillators.
Example Problem
Two capacitors (
, 
) are connected in series. Find the total capacitance.
- Formula:
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMzYiIGhlaWdodD0iMzkiIHZpZXdCb3g9IjAgMCAxMzYgMzkiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
- Substitute Values:
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDYiIGhlaWdodD0iNDAiIHZpZXdCb3g9IjAgMCAyNDYgNDAiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
- Result:
![\[ C_{\text{total}} = \frac{12}{5} = 2.4 \, \mu F \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNjIiIGhlaWdodD0iMzYiIHZpZXdCb3g9IjAgMCAxNjIgMzYiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-c9e56ad4426acd940c12e905c5594a01_l3.png "Rendered by QuickLaTeX.com")
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-17956aed36a02998aecc6c3666a03aa5_l3.png "Rendered by QuickLaTeX.com")
![\[ C_{\text{total}} = \frac{12}{5} = 2.4 \, \mu F \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-d39a1880f9670918378ec8c1537d377f_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes in Capacitor Calculations
- Forgetting to convert microfarads to farads in energy calculations
- Mixing up series and parallel formulas
- Neglecting the square in the energy formula
Practice Questions
- Calculate the energy stored in a
capacitor charged to 
- Explain the difference between series and parallel capacitor configurations
- Describe one real-world application of capacitors in electronics
capacitor charged to 