Capacitors and Capacitance

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Capacitors and Capacitance — Key Facts Capacitance: $C = \frac{Q}{V}$; unit: farad (F) = coulomb/volt Parallel plate capacitor: $C = \frac{\varepsilon_0 \varepsilon_r A}{d}$; $\varepsilon_r$ = relative permittivity Energy stored: $W = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV$ Charge on plates: $Q = CV$ ⚡ Exam tip: Capacitors in series share charge; capacitors in parallel share voltage

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Capacitors and Capacitance — JAMB Physics Study Guide Series combination: $$C_{eq} = \frac{C_1 C_2}{C_1 + C_2} \text{ (for two capacitors)}$$ $$C_{eq} = \frac{1}{\frac{1}{C_1} + \frac{1}{C_2} + …} \text{ (general)}$$ Voltage division: $V_1 = \frac{Q}{C_1}$, $V_2 = \frac{Q}{C_2}$ (same Q)

Parallel combination: $$C_{eq} = C_1 + C_2 + C_3 + …$$ Voltage is same across all: $V_1 = V_2 = V$

Dielectrics: inserting dielectric increases capacitance by factor $\varepsilon_r$; for parallel plate $C = \frac{\varepsilon_0 \varepsilon_r A}{d}$ Dielectric strength: maximum electric field before breakdown (typically 3-10 MV/m for air)

Time constant in RC circuits: $\tau = RC$; capacitor charges to 63% of final voltage in one $\tau$, and discharges to 37% remaining.

Common student mistakes: confusing series and parallel formulas (use the right one!); forgetting that adding dielectric increases capacitance; confusing capacitance with charge.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Capacitors and Capacitance — Comprehensive Physics Notes

Derivation of parallel plate capacitance: Consider two parallel plates each of area $A$, separated by distance $d$, with vacuum between them.

Electric field between plates (infinite plate approximation): $E = \frac{\sigma}{\varepsilon_0} = \frac{Q}{A\varepsilon_0}$

Potential difference: $V = Ed = \frac{Qd}{A\varepsilon_0}$

Therefore: $C = \frac{Q}{V} = \frac{Q}{Qd/(A\varepsilon_0)} = \frac{\varepsilon_0 A}{d}$

Energy density: Energy stored per unit volume in electric field: $$u = \frac{1}{2}\varepsilon_0 E^2 = \frac{1}{2}\varepsilon_0 \varepsilon_r E^2 \text{ (with dielectric)}$$

Charging and discharging of capacitor through resistor: Charging: $q = Q_0(1 - e^{-t/RC})$; $V = V_0(1 - e^{-t/RC})$ Discharging: $q = Q_0 e^{-t/RC}$; $V = V_0 e^{-t/RC}$

Time constant $\tau = RC$: at $t = \tau$, capacitor reaches 63.2% of maximum charge (or discharges to 36.8%).

Capacitor combinations — detailed: Three or more in series: $$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}$$ For $n$ identical capacitors $C_0$ in series: $C_{eq} = C_0/n$ For $n$ identical capacitors $C_0$ in parallel: $C_{eq} = nC_0$

Applications of capacitors:

• Flash photography: capacitor charges slowly through high resistance, discharges quickly through flash tube
• Smooth DC power supplies: capacitors filter ripple in rectifier circuits (typically 1000 μF to 4700 μF electrolytic)
• Timer circuits: RC combinations provide time delays
• Defibrillators: capacitors store energy (~360 J) and release it quickly to restart heart
• Tuned radio circuits: LC circuits select specific frequencies
• Power factor correction: large capacitors improve efficiency of AC power transmission

Capacitor dielectric types:

Dielectric	εᵣ (approx)	Typical use
Air	1.0	Variable capacitors in radios
Paper	2.5	Old radio circuits
Mica	5-7	High-frequency applications
Ceramic	10-100	Small SMD components
Glass	5-10	High-voltage applications
Electrolytic	10-100	Power supply filtering
Tantalum	25-35	Compact electronics

JAMB exam patterns:

• 2022 JAMB: Two capacitors 4 μF and 6 μF connected in series across 100 V; find charge on each
• 2021 JAMB: Energy stored in a 10 μF capacitor at 200 V
• 2020 JAMB: Effect of halving the plate separation on capacitance of parallel plate capacitor
• 2019 JAMB: Time constant in RC circuit with R = 1 MΩ and C = 4 μF

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📊 JAMB Exam Essentials

Detail	Value
Questions	180 MCQs (UTME)
Subjects	4 subjects (language + 3 for course)
Time	2 hours
Marking	+1 per correct answer
Score	400 max (used for university admission)
Registration	January – February each year

🎯 High-Yield Topics for JAMB

• Use of English (Grammar + Comprehension) — 60 marks
• Biology for Science students — 40 marks
• Chemistry (Organic + Physical) — 40 marks
• Physics (Mechanics + Optics) — 35 marks
• Mathematics (Algebra + Geometry) — 40 marks

📝 Previous Year Question Patterns

• Q: “The process of photosynthesis requires…” [2024 Biology]
• Q: “The electronic configuration of Fe is…” [2024 Chemistry]
• Q: “Find the value of x if 2x + 5 = 15…” [2024 Mathematics]

💡 Pro Tips

• Use of English carries the most weight — master grammar rules and comprehension strategies
• JAMB syllabus is your Bible — questions come directly from it. Download and use it.
• Past questions are highly predictive — repeat patterns appear every year
• For Science students, Biology and Chemistry are high-scoring if you study NCERT-level content

🔗 Official Resources

• JAMB Official
• JAMB Syllabus

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