Capacitance Formula, Unit, and How to Solve Numericals
Capacitance is a property of electric conductors or systems of conductors that describes their ability to store electrical charge. Whenever charge is separated between two conductors, one becomes positively charged and the other negatively charged, creating a potential difference. The amount of charge that can be stored per unit potential difference is called the capacitance.
Capacitance is mathematically defined as C = q / V, where C is the capacitance, q is the charge stored, and V is the potential difference between the conductors. The SI unit of capacitance is the farad (F), which is equal to one coulomb per volt. However, the farad is a very large unit. More commonly, smaller subunits like microfarad (μF, or 10⁻⁶ F) and picofarad (pF, or 10⁻¹² F) are used in practical electronics.
Capacitors are the devices in circuits that utilize capacitance as a principle. A capacitor consists of two plates (conductors) of large area separated by a thin layer of insulating material, or dielectric. When a battery or other source is connected, equal and opposite charges collect on the two plates, storing energy in the electric field between them.
Explanation and Key Formulas
When the conductors (capacitor plates) are charged, the capacitance depends on three main factors:
- Surface area of the plates (larger area = higher capacitance)
- Distance between the plates (smaller distance = higher capacitance)
- The nature of the dielectric material (greater dielectric constant = higher capacitance)
For a parallel plate capacitor: C = εA / d
C = Capacitance (in farads)
ε = Permittivity of the dielectric (ε₀ in vacuum/air, ε = ε₀εr with dielectric)
A = Area of one plate (in m²)
d = Distance between plates (in meters)
| Formula | Description | Unit |
|---|---|---|
| C = q / V | Definition of Capacitance | farad (F) |
| C = εA / d | Parallel Plate Capacitor | farad (F) |
| U = (1/2)CV² | Energy Stored in Capacitor | joule (J) |
The energy stored by a capacitor is the work performed in creating the charge separation. This energy is stored in the electric field between the plates.
If the voltage across a capacitor is V, the energy stored (U) is:
U = ½ C V²
Capacitors in Electrical Circuits
Capacitors are widely used in electrical and electronic circuits for various functions, such as energy storage, filtering, and timing. When two or more capacitors are combined, the total capacitance depends on whether they are connected in series or parallel.
| Configuration | Total Capacitance |
|---|---|
| Series | 1/C_total = 1/C₁ + 1/C₂ + ... |
| Parallel | C_total = C₁ + C₂ + ... |
When connected in an alternating current (AC) circuit, capacitors are charged and discharged every half cycle. The effectiveness of charge storage changes with frequency and the properties of the dielectric, a phenomenon known as dielectric loss, which results in some heat generation.
In a direct current (DC) circuit, once the capacitor is fully charged, no current flows (except for a tiny leakage current across the dielectric).
Physical Examples and Applications
- Camera flash units: Capacitors charge up and release energy rapidly to produce a flash.
- Radio tuning: Variable capacitors help select the station frequency.
- Power conditioning: Capacitors reduce voltage fluctuations and filter noise.
The first capacitor, called the Leyden jar, was a glass jar with metal foil and a water filling, used to store static electricity. Modern capacitors use different shapes, sizes, and dielectrics such as air, mica, ceramic, or electrolytic materials.
Sample Step-by-Step Problem
Example: Calculate the capacitance of a parallel plate capacitor with plate area 0.2 m², separation 2 mm, using air (ε₀ = 8.85 × 10⁻¹² C²/N·m²).
- Convert 2 mm to meters: d = 0.002 m.
- Apply the formula: C = ε₀ × (A/d)
= 8.85 × 10⁻¹² × (0.2 / 0.002)
= 8.85 × 10⁻¹² × 100
= 8.85 × 10⁻¹⁰ F - Capacitance = 8.85 × 10⁻¹⁰ farads
Key Properties Table
| Term | Definition | Unit |
|---|---|---|
| Capacitance | Ability to store electric charge per unit potential | farad (F) |
| Charge | Total electric charge on a conductor | coulomb (C) |
| Potential Difference | Energy needed per unit charge | volt (V) |
Capacitance is fundamentally important in understanding electrostatics, electricity, and in designing devices like capacitors for real-world circuits.
To learn about different types of capacitors, explore Capacitor Types. For numeric practice or energy-based calculations, see Energy Stored in a Capacitor. To study the effect of materials on capacitance, visit Effect of Dielectric on Capacitance.
Continue learning with Vedantu for expert guidance, additional practice, and deeper conceptual understanding of Physics and related topics.
FAQs on Capacitance in Physics: Definition, Formula, Units, and Examples
2. What is the SI unit of capacitance?
The SI unit of capacitance is the farad (F), where 1 farad = 1 coulomb per volt (1 F = 1 C/V). Common subunits are microfarad (μF), nanofarad (nF), and picofarad (pF).
3. What is the formula for the capacitance of a parallel plate capacitor?
For a parallel plate capacitor, the capacitance is given by:
C = ε₀ (A/d) in vacuum
C = ε₀ × εr (A/d) with a dielectric material
Where:
• ε₀ = vacuum permittivity
• εr = relative dielectric constant
• A = area of one plate
• d = separation between plates
4. How does a capacitor store energy?
A capacitor stores energy in the electric field created between its plates. The energy stored is given by:
U = (1/2)CV2
Where:
• U = energy (in joules)
• C = capacitance (in farads)
• V = potential difference (in volts)
5. What is the effect of a dielectric material on capacitance?
Inserting a dielectric material between the plates of a capacitor increases its capacitance by the dielectric constant (εr).
New capacitance formula:
C = ε0εr (A/d)
Where εr is always greater than 1, thus increasing the stored charge for the same voltage.
6. What is the difference between series and parallel combination of capacitors?
Series combination: The reciprocal of total capacitance is the sum of the reciprocals of individual capacitances:
1/Ceq = 1/C1 + 1/C2 + ...
Parallel combination: The total capacitance is the sum of all capacitances:
Ceq = C1 + C2 + ...
7. What factors affect the capacitance of a parallel plate capacitor?
The capacitance depends on:
• Area of the plates (A) – larger area means more capacitance
• Distance between the plates (d) – smaller distance increases capacitance
• Permittivity of the dielectric (ε) between plates – higher permittivity yields higher capacitance
8. What is the dimensional formula of capacitance?
The dimensional formula for capacitance is:
M-1 L-2 T4 A2
9. Give two real-life applications of capacitors.
Capacitors are widely used in:
• Camera flashes to release energy rapidly
• Electronic circuits for filtering, timing, and energy storage (e.g., mobile phones, computers)
10. How do you calculate the total charge stored in a capacitor?
The total charge (Q) stored is given by the formula:
Q = C × V
Where C is capacitance in farads and V is potential difference in volts.
11. Can you give an example of a numerical problem involving capacitance?
Yes, for example:
Q: Find the capacitance of a parallel plate capacitor with plate area 0.2 m2, plate separation 0.01 m, and air as dielectric (ε0 = 8.85 × 10-12 C2/N&mmiddot;m2).
Solution: C = ε0 (A/d) = 8.85 × 10-12 × (0.2/0.01) = 1.77 × 10-10 F.
12. What is the difference between charge, potential difference, and capacitance?
Charge (Q) is the electric quantity stored in a capacitor (measured in coulombs).
Potential difference (V) is the voltage between the capacitor plates (in volts).
Capacitance (C) is the ratio of charge stored to voltage applied and determines how much charge can be held at a given voltage (measured in farads).
