Capacitors & Dielectrics
Build parallel plate capacitors, insert dielectrics, and observe how capacitance, charge, and energy storage change.
Key Notes
A capacitor stores electrical energy in the electric field between two conductors separated by a dielectric.
Capacitance C = Q/V, where Q is charge and V is potential difference. Unit: Farad (F).
For a parallel plate capacitor: C = ε₀κA/d, where A is plate area, d is separation, κ is dielectric constant.
Inserting a dielectric increases capacitance by factor κ. This is because the dielectric reduces the effective electric field.
Energy stored in a capacitor: U = ½CV² = ½QV = Q²/(2C).
In series combination: 1/C_eq = 1/C₁ + 1/C₂ + ... (charge same, voltage divides).
In parallel combination: C_eq = C₁ + C₂ + ... (voltage same, charge divides).
The electric field between plates is uniform: E = V/d = σ/ε₀ (for parallel plates without edge effects).
Formulas
Capacitance (Parallel Plate)
Depends on area, separation, and dielectric.
Energy Stored
Energy in the electric field.
Series Combination
Equivalent capacitance decreases in series.
Parallel Combination
Equivalent capacitance increases in parallel.
Electric Field
Uniform field between parallel plates.
Force Between Plates
Attractive force between oppositely charged plates.
Important Points
When a dielectric is inserted with battery connected: V stays same, C increases → Q increases, U increases.
When a dielectric is inserted with battery disconnected: Q stays same, C increases → V decreases, U decreases.
The energy 'lost' when connecting two charged capacitors goes into heat and radiation: U_lost = ½(C₁C₂/(C₁+C₂))(V₁−V₂)².
Capacitors block DC but pass AC — this is because they charge fully under DC and current stops.
In JEE, capacitor-dielectric problems often test whether battery is connected or disconnected — read carefully!
The time constant for RC circuits is τ = RC. After 5τ, the capacitor is ~99% charged.
Capacitors & Dielectrics notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.