Reading Time: < 1 minuteCapacitance (
Energy Stored (
Capacitors: Understanding Their Role in Energy Storage and Circuits
What Are Capacitors?
Capacitors are passive electronic components that store electrical energy in an electric field between conducting plates separated by an insulator (dielectric).
Key Properties of Capacitors
Capacitance (
)
)The ability to store charge per unit voltage:
![\[ C = \frac{Q}{V} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-7bec45e18175968f23e7147d4302ac33_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Capacitance (F, Farads)
: Stored charge (C, Coulombs)- : Potential difference (V, Volts)
: Stored charge (C, Coulombs)
: Potential difference (V, Volts)Energy Stored ()
)The energy stored in a capacitor:
![\[ E = \frac{1}{2}CV^2 \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-bed59ea59e4478c1fb7d6b8586365fd0_l3.png "Rendered by QuickLaTeX.com")
Example Calculation:
A 
capacitor at 
stores:
![\[ E = \frac{1}{2} \times 50 \times 10^{-6} \times 10^2 = 2.5 \, \text{mJ} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-4847e83616dd3a474e029f637e97604b_l3.png "Rendered by QuickLaTeX.com")
Capacitor Configurations
Parallel Connection
Total capacitance adds directly:
![\[ C_{\text{total}} = C_1 + C_2 + \cdots \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-0e5878ba2d422c77cfa81f8175dd7e5b_l3.png "Rendered by QuickLaTeX.com")
Series Connection
Reciprocal of total capacitance:
![\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-6a20fe7014974335fba9e0fa395ef3c4_l3.png "Rendered by QuickLaTeX.com")
Practical Applications
Power Systems
- Power factor correction (industrial scale)
- Energy storage in camera flashes (
)
)Electronics
- Decoupling capacitors (0.1 μF typical for ICs)
- Filter circuits (RC time constant
)
)Example Problem
Two capacitors (
, 
) in parallel:
![\[ C_{\text{total}} = 4 + 6 = 10 \, \mu\text{F} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-1ebabcacde207d195260e1e8db8f785c_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes
- Using series formula for parallel connections (and vice versa)
- Forgetting
conversion for μF → F - Omitting the
factor in energy calculations
conversion for μF → F
factor in energy calculationsPractice Problems
- Calculate energy in a
capacitor at 
- Derive the series capacitance formula from
- Explain why capacitors block DC but pass AC signals
capacitor at 
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