Grade 10 electricity Fundamentals of Electricity – Capacitors and Capacitance Notes

Specific learning outcomes

1. Describe the principle of operation of a capacitor in an electric circuit.
2. Explain the characteristics of capacitive circuits (charging, discharging, time constant).
3. Select appropriate capacitors for a given application in electric circuits.
4. Analyse series and parallel connection of capacitors in circuits.
5. Appreciate the importance of capacitors in electrical appliances.
6. Identify categories: capacitor operation, capacitive circuit characteristics, capacitor selection, series/parallel connections, and applications.

1. What is a capacitor? (Simple idea)

A capacitor is a device that stores electric charge and energy in an electric field. It consists of two conducting plates separated by an insulating material (dielectric).

2. Principle of operation

When a capacitor is connected to a battery, electrons accumulate on one plate (negative), leaving the other plate positively charged. The dielectric stops current flow but allows an electric field to form between plates — this is where energy is stored.

Charging stops when the voltage across the capacitor equals the battery voltage. During discharge, the capacitor supplies charge to the circuit until its stored energy is used.

3. Capacitive circuit characteristics

• Charging and discharging: Currents flow while the capacitor charges or discharges, but no steady DC current flows through an ideal capacitor once fully charged.
• Time constant (RC): τ = R × C (seconds). It shows how fast charging/discharging happens. After time τ the voltage reaches about 63% of final value during charging.
• Voltage-current relation: I = C × (dV/dt). Rapid voltage changes cause large currents.
• Frequency behaviour: In AC circuits, capacitors pass alternating currents more easily at high frequency (reactance Xc = 1 / (2πfC)).

4. Common types of capacitors (useful at school level)

• Ceramic: Small values (pF–nF), non-polar, used in filters and decoupling.
• Electrolytic: Large values (µF–mF), polarized, used for smoothing DC supplies.
• Film (Polyester, Polypropylene): Good stability and low loss — used in timing and audio circuits.
• Tantalum: Small size for higher capacitance; polarized, used in compact electronics (careful with polarity).
• Motor Run/Start capacitors: Larger AC-rated capacitors used in fans and motors.

5. How to select a capacitor (practical checklist)

• Capacitance value (C): Choose value that gives required time constant, filtering, or coupling.
• Voltage rating: Must be greater than the maximum circuit voltage. For safety in DC, use at least 25–50% higher rating.
• Polarity: If electrolytic/tantalum, observe correct polarity (negative to lower potential).
• Tolerance: How much value may vary (±5%, ±10%).
• ESR and temperature: For power or audio, choose low ESR and appropriate temperature rating.
• Physical size and cost: Consider available space and budget (e.g., in radios, TVs, motor starters).

6. Series and parallel connection

How capacitances combine:

7. Simple circuits and classroom activities

• Activity A — Observe charging: Materials: battery (9V), resistor 470 kΩ or 1 MΩ, electrolytic 100 µF, LED (with series resistor 1 kΩ). Procedure: connect R and C in series to battery, measure time until LED dims after disconnecting battery. Estimate τ = RC and compare.
• Activity B — RC time constant measurement: Use stopwatch and a small capacitor (e.g., 10 µF) and resistor (100 kΩ). Charge capacitor and measure time to reach ~63% of final voltage (use simple voltmeter). Compare with τ = RC.
• Activity C — Smoothing a DC supply: Build a simple rectifier + capacitor (electrolytic). Observe the ripple on a small DC motor or LED brightness change with and without the capacitor.

8. Capacitors in common Kenyan household appliances

• Ceiling fan motors — run capacitors (improve torque and efficiency).
• Fridge and washing machine — start capacitors for single-phase motors.
• Radios, TVs, phone chargers — smoothing capacitors in power supplies.
• Inverters and solar charge controllers — large electrolytics for energy smoothing.
• Lighting (fluorescent) ballasts and LED driver circuits — capacitors used in filtering and power-factor correction.

9. Safety and good practice

• Always discharge capacitors (especially large electrolytics) before touching — short across terminals with a resistor first.
• Observe polarity on polarized capacitors; connecting backwards can cause heating or explosion.
• Use the correct voltage rating; never operate a capacitor above its rated voltage.
• Store and solder capacitors carefully — heat can damage some types (use short soldering time).

10. Short assessment (for classroom or homework)

1. Define capacitance and write its unit.
2. Calculate the equivalent capacitance of 3 capacitors in parallel: 2µF, 5µF, 10µF.
3. Find the equivalent capacitance of two capacitors in series: 6µF and 3µF.
4. A 100µF capacitor is connected to 12 V. Find the charge stored and energy stored.
5. Explain why electrolytic capacitors are not used where polarity may reverse.

Answers (brief)

• Capacitance is C = Q/V; unit is the farad (F).
• Parallel: C = 2 + 5 + 10 = 17 µF.
• Series: 1/C = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 → C = 2 µF.
• Q = C V = 100×10^-6 × 12 = 1.2×10^-3 C (1.2 mC). Energy = 1/2 C V^2 = 0.5 × 100×10^-6 × 144 = 7.2×10^-3 J (7.2 mJ).
• Electrolytics are polarized — reversing polarity can damage the dielectric and cause leakage, heating or explosion.

Glossary (quick)

• Capacitance: Ability to store charge per volt (C in farads).
• Dielectric: Insulating material between capacitor plates.
• ESR: Equivalent series resistance — resistance inside the capacitor.
• Time constant (τ): RC value that sets charging/discharging speed.