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 (CCC)
Capacitance measures the ability of a capacitor to store charge per unit voltage:
C=QVC = \frac{Q}{V}C=VQ
Where:
- CCC: Capacitance (FFF, Farads).
- QQQ: Charge (CCC, Coulombs).
- VVV: Voltage (VVV, Volts).
Energy Stored in a Capacitor
The energy (EEE) stored is given by:
E=12CV2E = \frac{1}{2}CV^2E=21CV2
Example: A 100 μF100 \, \mu F100μF capacitor is charged to 10 V10 \, \text{V}10V. Find the energy stored.
- Use the formula: E=12⋅100×10−6⋅102=0.05 JE = \frac{1}{2} \cdot 100 \times 10^{-6} \cdot 10^2 = 0.05 \, \text{J}E=21⋅100×10−6⋅102=0.05J
Capacitor Configurations
Series Configuration
Capacitance decreases:
1Ctotal=1C1+1C2+…\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dotsCtotal1=C11+C21+…
Parallel Configuration
Capacitance increases:
Ctotal=C1+C2+…C_{\text{total}} = C_1 + C_2 + \dotsCtotal=C1+C2+…
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 (C1=4 μFC_1 = 4 \, \mu FC1=4μF, C2=6 μFC_2 = 6 \, \mu FC2=6μF) are connected in series. Find the total capacitance.
- Formula:
1Ctotal=1C1+1C2\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2}Ctotal1=C11+C21
- Substitute Values:
1Ctotal=14+16=312+212=512\frac{1}{C_{\text{total}}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}Ctotal1=41+61=123+122=125
- Result:
Ctotal=125=2.4 μFC_{\text{total}} = \frac{12}{5} = 2.4 \, \mu FCtotal=512=2.4μF
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 50 μF50 \, \mu F50μF capacitor charged to 12 V12 \, \text{V}12V.
- Explain the difference between series and parallel capacitor configurations.
- Describe one real-world application of capacitors in electronics.