Quick Revision
Last-day preparation. Everything in one place. Flashcards, formula dump, memory tricks. Don't try to learn new things — reinforce what you know.
Tool 01
🧠 Flashcard Mode
Click card to reveal answer. Use arrows to navigate. 20 cards covering all exam topics.
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Tool 02
⚡ One-Page Summary
📐 Core Formulas
Capacitance
C = Q/V = ε₀A/d
Energy
U = ½CV² = Q²/2C
With Dielectric
C = Kε₀A/d
Series
1/C = 1/C₁ + 1/C₂
Parallel
C = C₁ + C₂
RC Time Constant
τ = RC
🔬 Key Concepts
- C depends only on geometry & medium
- Series: same Q, voltage adds
- Parallel: same V, charge adds
- Battery ON: V constant when anything changes
- Battery OFF: Q constant when anything changes
- Dielectric increases C by K
- Conducting slab: C = ε₀A/(d-t)
- Dielectric slab: C = ε₀A/(d-t+t/K)
- Energy density: u = ½ε₀E²
- Force on plates: F = Q²/2ε₀A
- Wheatstone balance: C₁/C₂ = C₃/C₄
- Charging efficiency = 50% always
⚠️ Never Forget
½ in energy formula
U = ½CV² NOT CV²
U = ½CV² NOT CV²
Series: same Q
Only if initially uncharged
Only if initially uncharged
E between plates
σ/ε₀ (NOT σ/2ε₀)
σ/ε₀ (NOT σ/2ε₀)
Dimensions of C
[M⁻¹L⁻²T⁴A²]
[M⁻¹L⁻²T⁴A²]
Force: factor of 2
F = Q²/2ε₀A (not Q²/ε₀A)
F = Q²/2ε₀A (not Q²/ε₀A)
Tool 03
📊 Dielectric Master Table
The most tested table. Memorize it. Use it in every exam.
| Quantity | Battery ON (V=const) | Battery OFF (Q=const) | Trend |
|---|---|---|---|
| Capacitance C | → KC₀ (increases ×K) | → KC₀ (increases ×K) | Always ↑ |
| Charge Q | → KQ₀ (increases ×K) | → Q₀ (constant) | Depends on mode |
| Voltage V | → V₀ (constant) | → V₀/K (decreases) | Depends on mode |
| Electric Field E | → E₀ (constant, = V/d) | → E₀/K (decreases) | Depends on mode |
| Energy U | → KU₀ (increases ×K) | → U₀/K (decreases) | Opposite directions |
🎯 Memory Shortcut
Battery ON: Think "C and everything goes UP by K" (C, Q, U all × K). V is held fixed by battery. E = V/d also constant.
Battery OFF: Think "C goes up, but V and U get squeezed down by K (÷ K)". Q is locked. E = Q/ε₀KA → drops.
Battery OFF: Think "C goes up, but V and U get squeezed down by K (÷ K)". Q is locked. E = Q/ε₀KA → drops.
Tool 04
🧠 Memory Tricks & Mnemonics
Series vs Parallel
Series = sharing one pizza (less each). Parallel = each gets their own pizza (more total).
C vs d Relationship
C and d are inversely proportional. Think: closer plates = stronger pull = more charge stored = higher C.
50% Efficiency Rule
Battery → Capacitor → Always 50% efficiency. Half to capacitor, half to heat. No way around it.
Energy Density
u = ½ε₀E² "Half epsilon E-squared" — same as ½mv² for kinetic energy. The ½ is always there.
Bridge Balance
C₁/C₂ = C₃/C₄ → bridge balanced → middle capacitor has NO charge. Like a balanced Wheatstone.
Voltage in Series
V ∝ 1/C in series. Smaller capacitor gets MORE voltage. Counter-intuitive — remember it.
RC Charging
At t=τ: 63.2% charged. At t=2τ: 86.5%. At t=5τ: 99.3%. (1-1/e, 1-1/e², practically full)
The "Factor of 2" Rule
Force on plates = Q²/2ε₀A. Energy = ½CV². Time constant has no ½. Watch the ½ carefully.
Tool 05
📋 Complete Formula Dump
Everything in one scrollable list. Scan this 5 minutes before the exam.
Basic & Geometry
C = Q/V
C = ε₀A/d (air)
C = Kε₀A/d (dielectric)
C = 4πε₀ab/(b-a) [spherical]
C = 4πε₀R [isolated sphere]
C = ε₀A/(d-t) [conducting slab]
C = ε₀A/(d-t+t/K) [dielectric slab]
Combinations
Series: 1/C = Σ(1/Cᵢ)
Parallel: C = ΣCᵢ
2 in series: C₁C₂/(C₁+C₂)
V_common = (C₁V₁+C₂V₂)/(C₁+C₂)
Bridge: C₁/C₂ = C₃/C₄ → balanced
Energy & Force
U = ½CV² = Q²/2C = ½QV
u = ½ε₀E² [energy density]
ΔU = ½(C₁C₂/C₁+C₂)(V₁-V₂)²
F = Q²/2ε₀A [force on plate]
η = 50% [charging efficiency]
RC Circuits
τ = RC
q(t) = CV(1-e^(-t/RC))
q(t) = Q₀e^(-t/RC)
t₁/₂ = 0.693RC
I₀ = V/R at t=0
Dimensions
[C] = [M⁻¹L⁻²T⁴A²]
[ε₀] = [M⁻¹L⁻³T⁴A²]
[E field] = [MLT⁻³A⁻¹]
5-Minute Pre-Exam Revision
Read these 10 lines. If you know all 10, you're ready.
- C = Q/V; unit = Farad; [M⁻¹L⁻²T⁴A²]
- Parallel plate: C = ε₀A/d (air), Kε₀A/d (dielectric)
- Series: 1/C = sum of reciprocals. Same Q on each.
- Parallel: C = sum. Same V across each.
- Energy = ½CV² = Q²/2C = ½QV
- Battery ON → V const. Battery OFF → Q const.
- Dielectric in (batt ON): C,Q,U all ×K; V,E constant
- Dielectric in (batt OFF): C×K, V/K, U/K; Q constant
- τ = RC. At t=τ: 63.2% charged.
- Bridge balanced: C₁/C₂ = C₃/C₄ → middle cap = 0 charge
"You've done the work. Now trust it. Don't try to learn new things 5 minutes before the exam. Confidence + Focus = Full Marks."
— Final Revision Mindset
🎯 Mental Approach
Every capacitor problem has a KEY question:
"Is the battery connected?"
Answer that first. Then everything follows.
"Is the battery connected?"
Answer that first. Then everything follows.
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