Capacitors – Complete Formula, Traps & Question Profiling (JEE Main Only)
1. Basic Concept of Capacitor
- Capacitor: Device to store electric charge
- Consists of two conductors separated by dielectric
C = Q / V
- SI unit → Farad (F)
- 1 μF = 10⁻⁶ F
2. Parallel Plate Capacitor
C = ε₀ A / d
- A → area of plates
- d → separation
With dielectric (k):
C = k ε₀ A / d
3. Effect of Dielectric
- Capacitance increases k times
- Electric field reduces: E = E₀ / k
- Potential reduces: V = V₀ / k
Dielectric constant:
k = ε / ε₀
4. Series & Parallel Combination
Series:
1/Ceq = 1/C₁ + 1/C₂ + ...
- Charge same on each capacitor
- V distributes
Parallel:
Ceq = C₁ + C₂ + ...
- Potential same
- Charge distributes
5. Energy Stored in Capacitor
U = ½ C V²
U = Q² / (2C)
U = ½ QV
Energy density:
u = ½ ε E²
6. Capacitor with Battery Connected / Disconnected
Battery connected:
- V constant
- Q increases with dielectric
- Energy increases
Battery disconnected:
- Q constant
- V decreases
- Energy decreases
7. Capacitor with Partially Filled Dielectric
- Treat as series combination
- Area-wise filling → parallel combination
Key JEE idea: Identify orientation of dielectric first
8. Electric Field Between Plates
E = V / d
Without dielectric: E₀ = σ / ε₀
With dielectric: E = σ / ε
9. Force Between Capacitor Plates
F = ½ ε₀ A E²
- Always attractive
- Independent of charge sign
10. Charging & Discharging (Basic)
- Q(t) = Q₀(1 − e⁻ᵗ/RC)
- V(t) = V₀(1 − e⁻ᵗ/RC)
- Time constant τ = RC
JEE Main: Mostly conceptual, not graph-heavy
11. JEE Main Question Profiling
| Question Type | JEE Focus | Common Trap |
|---|---|---|
| Direct C formula | ε₀A/d | Forgetting dielectric |
| Series/Parallel | Charge vs voltage logic | Using wrong combination |
| Dielectric insertion | Battery ON/OFF | Wrong constant assumption |
| Energy change | ½CV² logic | Using Q constant wrongly |
| Partially filled dielectric | Geometry understanding | Not splitting capacitor |
| Force between plates | E² dependence | Using Coulomb force |
12. JEE Main Weightage Insight
- 1–2 questions guaranteed
- Mostly formula + logic based
- High ROI chapter if concepts clear
StudyBeacon • JEE Main Physics • Capacitor Master Sheet
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