8.1 Capacitor Operation & Factors Affecting Capacitance

8.1 Capacitor Operation & Factors Affecting Capacitance

Quick Answer: A capacitor stores charge on two conductors separated by an insulator (dielectric). C = Q / V, so capacitance is charge stored per volt. Increase plate area or dielectric constant, or add more plates, and C rises; increase plate separation and C falls. Always stay below the marked working voltage.

CAAS SAR-66 Module 3 topic 3.9 Capacitance / capacitor sits between resistance and magnetism in the electrical fundamentals syllabus. Aircraft systems use capacitors for filtering, timing, coupling, and energy storage on DC buses and AC equipment. Before you combine capacitors in series or parallel, you must understand what one capacitor is and what changes its farad value.

What a Capacitor Does

A basic capacitor has:

1. Two conductive plates (or foils, films, or electrodes).
2. A dielectric — an insulating material between the plates (air, paper, mica, ceramic, plastic film, oxide layer, and so on).

When a DC voltage is applied, electrons are driven onto one plate and removed from the other. Opposite charges accumulate. The dielectric prevents a continuous DC conduction path (ideally), so after the transient charging current dies, steady DC current through an ideal capacitor is zero. The stored electrostatic field holds the charge until the circuit discharges it through a path.

Charge polarity: The plate connected toward the more negative supply accumulates excess electrons (negative charge). The other plate is deficient in electrons (positive charge). The magnitude of charge on each plate is the same; we call that magnitude Q.

Definition: C = Q / V

Capacitance C is defined as:

C = Q / V

Rearrangements you must use fluently:

• Q = C × V
• V = Q / C

Physical reading: A 1 F capacitor would store 1 C of charge at 1 V. Practical capacitors are tiny fractions of a farad, so Module 3 uses submultiples:

Worked example 1 — find C. A capacitor holds Q = 200 µC at V = 50 V.

Convert: Q = 200 × 10⁻⁶ C = 2.0 × 10⁻⁴ C.

C = Q / V = (2.0 × 10⁻⁴) / 50 = 4.0 × 10⁻⁶ F = 4 µF.

Worked example 2 — find charge. A 10 µF capacitor is charged to 28 V (aircraft DC bus order of magnitude).

Q = C × V = 10 × 10⁻⁶ × 28 = 2.8 × 10⁻⁴ C = 280 µC.

Worked example 3 — find voltage. A 0.47 µF capacitor stores 94 µC.

V = Q / C = (94 × 10⁻⁶) / (0.47 × 10⁻⁶) = 200 V.

Unit discipline matters: mixing µC with F without converting produces nonsense voltages. Convert both Q and C to coulombs and farads, or keep consistent micro-units carefully (µC / µF = V).

Parallel-Plate Factors Affecting Capacitance

For a simple parallel-plate capacitor in SI form:

C = ε₀ εᵣ A / d

You rarely need the numerical value of ε₀ on Module 3. You do need the proportional rules:

Area

Larger overlapping area → more charge can be stored at the same voltage → higher C. Doubling A doubles C.

Worked example 4 — area. A capacitor has C₁ = 100 pF. Plate overlap area is doubled; d and dielectric unchanged. New C = 200 pF.

Distance (separation)

Smaller gap → stronger field for a given V and more charge for that V → higher C. Doubling d halves C. Pushing plates closer raises C until dielectric strength or mechanical limits intervene.

Worked example 5 — separation. C₁ = 0.22 µF. Separation is reduced to one-third. New C = 0.22 × 3 = 0.66 µF.

Dielectric constant

Replacing air (εᵣ ≈ 1) with a material of εᵣ = 5 multiplies C by about 5, same geometry. Higher-εᵣ dielectrics pack more capacitance into a smaller package — why ceramics and specialised films appear in avionics boards.

Worked example 6 — dielectric swap. An air-spaced capacitor is 50 pF. Insert a dielectric with εᵣ = 4 (same A and d). New C ≈ 200 pF.

Number of plates

Multi-plate capacitors interleave several plates with dielectric between each adjacent pair. Each facing pair forms a capacitor; the sections act in parallel, so total C rises with the number of dielectric gaps (roughly C ∝ (n − 1) for n interleaved plates of equal area, same d).

Exam phrasing: “Increasing the number of plates increases capacitance” is the Module 3 statement to remember, alongside area up / distance down / dielectric constant up.

Working Voltage / Voltage Rating

Every capacitor has a working voltage (WV), DC working voltage (WVDC), or similar voltage rating. This is the maximum continuous voltage the manufacturer rates the dielectric to withstand under stated conditions.

• Exceeding the rating risks dielectric breakdown: the insulator punches through, the capacitor may short, open, leak heavily, or fail violently (especially electrolytics).
• Always select a rating above the highest voltage the capacitor will see, including spikes and AC peaks where relevant.
• On a 28 V DC aircraft bus filter, a 16 V capacitor is unsafe; a 35 V or 50 V part is the usual thinking — rating must clear the actual voltage with margin.

Worked example 7 — rating check. A timing capacitor sits across a 24 V DC rail that can surge to 30 V. A part marked 25 V WVDC is inadequate for the surge; choose ≥ 35 V (or the design minimum specified).

Capacitance value and voltage rating are independent markings. A 10 µF / 16 V part and a 10 µF / 63 V part store the same charge at 10 V, but only the higher-rated part survives higher applied voltage.

Charge, Voltage, and Current Behaviour (Preview)

While charging from a DC source through resistance, current flows until V_capacitor equals the applied voltage (ideal case). Once charged and open-circuited, an ideal capacitor holds Q; real parts slowly leak. Connecting a charged capacitor across a low resistance produces a discharge current — energy leaves the electrostatic field as heat and/or work. Section 8.3 develops the RC time constant and energy ½CV²; here the exam core is C = Q/V plus the four construction factors and voltage rating.

Factor Summary for Module 3

Trap: Raising voltage stores more charge (Q = CV) but does not redefine the capacitance of a linear capacitor. C is the constant of proportionality, not something that “grows” because you applied more volts (within the linear, undamaged range).

Master C = Q/V, the µF/nF/pF conversions, the area–distance–dielectric–plates rules, and working-voltage discipline. Those tools unlock series/parallel networks and RC timing in the next sections.