E3: Capacitors & Inductors
Capacitance, charge storage, RC circuits, inductance and energy storage
Capacitors & Inductors
Capacitance, charge storage, RC circuits, inductance and energy storage
Key Fact: Capacitance C = Q/V, measured in farads (F); a capacitor stores charge on parallel plates separated by a dielectric.
Key Fact: The energy stored in a capacitor is E = ½CV² = ½QV.
Key Fact: In an RC charging circuit, V_C rises exponentially: V_C = V_supply(1 − e^(−t/RC)).
Key Fact: The time constant τ = RC is the time for the capacitor to reach 63.2% of its final voltage when charging.
Key Fact: During discharge, V_C = V_initial × e^(−t/RC); after 5τ the capacitor is effectively fully discharged.
Key Fact: Inductance L is measured in henrys (H); an inductor stores energy in its magnetic field.
Key Fact: The energy stored in an inductor is E = ½LI².
Key Fact: An inductor opposes changes in current: V = L × dI/dt (back EMF).
Key Fact: Capacitors block DC at steady state but pass AC; inductors pass DC at steady state but oppose AC.
Key Fact: Dielectric material between capacitor plates increases capacitance by reducing the electric field.
Key Fact: Increasing plate area or decreasing plate separation increases capacitance.
Key Fact: Inductors in series add: L_total = L1 + L2; in parallel: 1/L_total = 1/L1 + 1/L2.
📋 Key Vocabulary and Concepts
For Capacitors & Inductors, you must know:
- Capacitance: The ability of a component to store charge per unit voltage, measured in farads.
- Time constant: τ = RC; the time for an RC circuit to reach 63.2% of its final value during charging.
- Dielectric: An insulating material between capacitor plates that increases capacitance.
- Inductance: The property of a coil that opposes changes in current, measured in henrys.
- Back EMF: The voltage induced across an inductor that opposes the change in current producing it.
- Exponential decay: A decrease in quantity where the rate of change is proportional to the current value.
❓ Practice Questions
Q: A 100 μF capacitor is charged to 10 V. How much charge is stored?
Q: What is the time constant of a circuit with R = 10 kΩ and C = 20 μF?
Q: How much energy is stored in a 47 μF capacitor charged to 12 V?
Q: What is the energy stored in a 10 mH inductor carrying 2 A?
Q: After how many time constants is a discharging capacitor considered fully discharged?
✅ Answers
- Q = CV = 100 × 10⁻⁶ × 10 = 1 × 10⁻³ C = 1 mC.
- τ = RC = 10 × 10³ × 20 × 10⁻⁶ = 0.2 s.
- E = ½CV² = 0.5 × 47 × 10⁻⁶ × 144 = 3.384 × 10⁻³ J ≈ 3.4 mJ.
- E = ½LI² = 0.5 × 10 × 10⁻³ × 4 = 20 × 10⁻³ J = 20 mJ.
- After 5τ, the capacitor voltage has fallen to less than 1% of its initial value and is considered fully discharged.
🎯 Exam Tips
- Always convert units: μF to F (×10⁻⁶), mH to H (×10⁻³) before substituting into formulas.
- State the exponential formula before substituting values in RC circuit questions.
- Remember: at t = τ, charging reaches 63.2%; after 5τ it is ~99.3% charged.
- For energy calculations, use E = ½CV² for capacitors and E = ½LI² for inductors.
- Sketch the exponential charging/discharging curve to support your answer when asked to describe behaviour.
📝 Exam Technique
GCSE Electronics Exam Tips — Capacitors & Inductors:
1. For Capacitors & Inductors questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Capacitors & Inductors, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
1. For Capacitors & Inductors questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Capacitors & Inductors, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
⚠️ Common Errors
✗ Forgetting to convert μF or mF to farads before calculation. ✓ Always convert: 100 μF = 100 × 10⁻⁶ F.
✗ Using E = CV² instead of E = ½CV² for capacitor energy. ✓ The correct formula is E = ½CV², which includes the factor of ½.
✗ Saying a capacitor is fully charged after one time constant. ✓ After one time constant (τ), the capacitor has reached only 63.2% of its final voltage.
✗ Confusing capacitor and inductor behaviour with DC at steady state. ✓ A capacitor blocks DC at steady state; an inductor acts as a short circuit to DC at steady state.
✍️ Model Answer
Full-Mark Response
Describe how a capacitor charges and discharges in an RC circuit, explaining the significance of the time constant.
When a capacitor charges through a resistor from a supply voltage V_s, the voltage across the capacitor rises exponentially: V_C = V_s(1 − e^(−t/RC)). The current starts at its maximum value I = V_s/R and decays exponentially. The time constant τ = RC is the time taken for the capacitor voltage to reach 63.2% of V_s. After 5τ the capacitor is effectively fully charged (~99.3%). During discharge, V_C = V_0 × e^(−t/RC), where V_0 is the initial voltage. The voltage falls to 36.8% of V_0 after one time constant and is effectively zero after 5τ. A larger R or C gives a larger time constant, meaning slower charging and discharging. The exponential behaviour occurs because the charging rate depends on the remaining voltage difference, which decreases as the capacitor charges.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of capacitors & inductors, including electronic components, circuit theory and systems concepts relevant to WJEC Eduqas C690QS.
AO2 (Application): Apply knowledge and understanding of capacitors & inductors to analyse, design and construct electronic circuits and systems.
AO3 (Evaluation): Evaluate electronic circuits and systems, making reasoned judgements about design choices, performance and practical considerations, constructing supported arguments.
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