8.2 Series/Parallel Capacitors & Types

8.2 Series/Parallel Capacitors & Types

Quick Answer: Parallel: add capacitances (C_T = C1 + C2 + …); same voltage on each. Series: reciprocals add (1/C_T = 1/C1 + 1/C2 + …); same charge through the string; voltages split as V = Q/C. Know major capacitor types (ceramic, film, mica, electrolytic, variable) and how markings/colour codes show value — and never reverse a polarised electrolytic.

Once you can define C = Q/V for one part, Module 3 expects you to reduce networks and recognise what physical type you are looking at on a board or in a parts list.

Parallel Capacitors

When capacitors share the same two nodes, they are in parallel.

C_T = C1 + C2 + C3 + …

• Every capacitor has the same voltage as the supply across the parallel group.
• Total charge stored is the sum of the individual charges: Q_T = Q1 + Q2 + … = C1V + C2V = C_T V.
• Parallel connection is how multi-plate stacks increase C: more area essentially in parallel.

Worked example 1 — parallel total. C1 = 10 µF, C2 = 22 µF, C3 = 4.7 µF, all in parallel.

C_T = 10 + 22 + 4.7 = 36.7 µF.

Worked example 2 — parallel charge. Those three on a 12 V rail:

Q_T = C_T × V = 36.7 × 10⁻⁶ × 12 ≈ 4.40 × 10⁻⁴ C.

Alternatively: Q1 = 120 µC, Q2 = 264 µC, Q3 = 56.4 µC; sum ≈ 440 µC — same result.

Voltage rating note: In parallel, each capacitor must individually withstand the full applied voltage. Adding a second capacitor does not reduce the voltage each dielectric sees.

Series Capacitors

When capacitors are connected end-to-end in a single path, they are in series.

1 / C_T = 1/C1 + 1/C2 + 1/C3 + …

Special cases:

• Two capacitors: C_T = (C1 × C2) / (C1 + C2)
• n equal capacitors of value C: C_T = C / n

Series behaviour mirrors parallel resistors in the reciprocal pattern — do not confuse with series resistors (which add directly).

Charge in series: The same charge magnitude Q appears on each series capacitor (for a series string charged from a DC source through the string). Then:

V1 = Q / C1, V2 = Q / C2, and V_supply = V1 + V2 + … (KVL).

Smaller C takes larger voltage share because V = Q/C with Q common.

Worked example 3 — two in series. C1 = 4 µF, C2 = 12 µF.

C_T = (4 × 12) / (4 + 12) = 48 / 16 = 3 µF.

Check: C_T is less than the smallest (4 µF) — always true for series capacitors greater than zero.

Worked example 4 — series voltages. The 4 µF and 12 µF string is charged from 48 V DC (steady state).

C_T = 3 µF → Q = C_T × V = 3 × 10⁻⁶ × 48 = 144 µC.

V1 (across 4 µF) = Q / C1 = 144 / 4 = 36 V.

V2 (across 12 µF) = 144 / 12 = 12 V.

Check: 36 + 12 = 48 V. The smaller capacitor took three-quarters of the voltage.

Worked example 5 — three equal series. Three 30 µF capacitors in series: C_T = 30 / 3 = 10 µF. On 30 V total, each drops 10 V if they are identical.

Voltage rating in series: Series connection can share voltage, but unequal capacitances (or unequal leakage) can leave one part over-voltaged. Design practice often uses equal values, bleed resistors, or ratings that still clear worst-case share. For Module 3 calculations, apply V = Q/C with common Q unless the stem states otherwise.

Combination Networks

Reduce inner series or parallel groups first, then combine outward — same discipline as resistor networks, with capacitor formulae substituted.

Worked example 6 — mix. Two 10 µF in parallel (= 20 µF) in series with a 20 µF:

C_T = (20 × 20) / (20 + 20) = 10 µF.

Capacitor Types, Construction & Function

Polarity: Aluminium and tantalum electrolytics are polarised. Reverse voltage destroys the oxide dielectric. Non-polar film and most ceramics can be connected either way (within voltage rating).

Function themes on aircraft/avionics training boards:

• Filtering / smoothing — large electrolytics on DC supplies.
• Decoupling — ceramics near ICs, short leads.
• Timing / RC networks — film or ceramic with resistors (see §8.3).
• Coupling / blocking — pass AC changes while blocking steady DC.
• Trimming — adjustable capacitors in RF or sensor circuits.

Colour Coding & Marking Overview

Unlike resistors, capacitor marking schemes vary by era and type. Module 3 expects familiarity with the idea of colour bands or printed codes for value (often in pF), plus separate voltage and tolerance information.

Typical colour-code pattern (training overview — many film/ceramic antiques and teaching charts):

• Coloured bands or dots encode significant digits and a multiplier, analogous in spirit to resistor bands, often yielding a value in picofarads.
• An extra band or mark may indicate tolerance or temperature characteristic.
• Voltage rating may be a separate band, printed number (for example “63V”), or body size convention — never assume colour alone states voltage on modern parts.

Modern printed markings (more common in practice):

Three-digit EIA-style codes: first two digits are significant figures; third digit is the power-of-ten multiplier in pF (same idea as resistor multipliers, but base unit is usually pF for ceramics).

Worked decode. Marking 105 → 10 × 10⁵ pF = 1 000 000 pF = 1 µF.

Electrolytic can markings: Capacitance and voltage printed explicitly (for example 470 µF 35 V); the longer lead or “−” stripe marks polarity — stripe usually indicates the negative terminal on aluminium electrolytics.

Exam Habits

1. Identify series vs parallel before writing a formula.
2. For series, compute C_T, then Q = C_T V_total, then each V_i = Q / C_i.
3. Reject any series C_T larger than the smallest capacitor.
4. Match type to polarity and application (electrolytic ≠ non-polar film).
5. Read markings: digits/multiplier (often pF) and confirm voltage rating separately.

Series/parallel arithmetic plus type recognition and marking literacy complete the “static” capacitor skill set before RC dynamics in §8.3.