Capacitors and Dielectrics
Parallel plate capacitance, combinations, energy stored and effect of a dielectric. (Physics › Electrostatics, NEET UG syllabus.)
What is Capacitors and Dielectrics?
A device used to store electric charge and electrical energy in an electric field.
Key formula / rule: Capacitance Definition
Key points
- Define capacitance and state its SI unit.
- Derive the capacitance for a parallel plate capacitor.
- Calculate equivalent capacitance for series and parallel combinations.
- Compute the energy stored in a capacitor.
Common exam trap
Confusing series and parallel combination formulas for capacitors with those for resistors.
Definitions
- Term
Capacitor
- Meaning
A device used to store electric charge and electrical energy in an electric field.
- Term
Capacitance
- Meaning
The ability of a capacitor to store charge, defined as the ratio of the magnitude of charge on either plate to the potential difference between the plates (C = Q/V).
- Term
Dielectric
- Meaning
An electrically insulating material placed between the plates of a capacitor to increase its capacitance and dielectric strength.
- Term
Dielectric Constant (K)
- Meaning
A dimensionless quantity that indicates how many × the capacitance increases when a dielectric is inserted, compared to vacuum (K = C/C₀).
- Term
Dielectric Strength
- Meaning
The maximum electric field intensity that an insulating material can withstand without undergoing electrical breakdown.
Learning objectives
Define capacitance and state its SI unit.
Derive the capacitance for a parallel plate capacitor.
Calculate equivalent capacitance for series and parallel combinations.
Compute the energy stored in a capacitor.
Explain the effect of introducing a dielectric material on capacitance and other electrical quantities.
Solve problems involving capacitors with and without dielectrics in various configurations.
Formulae
- Name
Capacitance Definition
- Note
Q is the magnitude of charge on either plate, V is the potential difference between plates.
- Expression
C = Q/V
- Name
Capacitance of a Parallel Plate Capacitor (in vacuum/air)
- Note
ε₀ is permittivity of free space, A is plate area, d is plate separation.
- Expression
C₀ = ε₀A/d
- Name
Capacitance of a Parallel Plate Capacitor (with dielectric)
- Note
K is the dielectric constant of the material.
- Expression
C = Kε₀A/d = KC₀
- Name
Equivalent Capacitance (Series Combination)
- Note
Charge (Q) is same across each capacitor, potential difference (V) divides.
- Expression
1/Ceq = 1/C₁ + 1/C₂ + ...
- Name
Equivalent Capacitance (Parallel Combination)
- Note
Potential difference (V) is same across each capacitor, charge (Q) divides.
- Expression
Ceq = C₁ + C₂ + ...
- Name
Energy Stored in a Capacitor
- Note
Energy is stored in the electric field between the plates.
- Expression
U = ½CV² = ½Q²/C = ½QV
- Name
Energy Density of Electric Field
- Note
ε is the permittivity of the medium (ε = Kε₀), E is the electric field strength.
- Expression
u = ½εE²
Prerequisites
Basic understanding of electric charge and Coulomb's Law.
Knowledge of electric field and electric potential.
Understanding of Gauss's Law and its applications.
Familiarity with potential difference and work done by electric fields.
Common mistakes
Confusing series and parallel combination formulas for capacitors with those for resistors.
Incorrectly applying the effect of dielectric when the battery is connected vs. disconnected.
Using incorrect units for area (A) or distance (d) in capacitance formulas (e.g., cm instead of m).
Forgetting the factor of ½ in energy stored formulas.
Assuming charge (Q) is always constant or voltage (V) is always constant when a dielectric is inserted.
Keywords
Capacitor
Capacitance
Farad
Dielectric
Dielectric Constant
Series Combination
Parallel Combination
Energy Storage
Electric Field
Permittivity
Practice preview
A parallel plate capacitor is charged by a battery and then the battery is disconnected. If a dielectric slab is inserted between the plates, which of the following statements is INCORRECT?…
medium
A parallel plate capacitor has plates of area A and separation d. It is filled with two dielectric slabs. The first slab has a dielectric constant K1 and thickness d/2, and the second slab has a dielectric constant K2 an…
hard
A capacitor of 100 microfarad is charged to a potential difference of 200 V. The energy stored in the capacitor is:…
medium