6.3 Series/Parallel Resistors, Potentiometers & Rheostats

6.3 Series/Parallel Resistors, Potentiometers & Rheostats

Quick Answer: Series: add resistances; same I; voltages share by proportion. Parallel: add reciprocals (or use product-over-sum for two); same V across branches; currents share. A potentiometer uses three terminals as an adjustable divider; a rheostat uses the track as a two-terminal variable R to control current.

After resistivity and colour codes, Module 3 asks you to combine resistors and to explain adjustable types. These skills feed every later DC network and many sensor-bias circuits on aircraft.

Series Resistors

For resistors in series (end-to-end, one path):

R_total = R₁ + R₂ + R₃ + …

Properties:

• Same current through every series element.
• Voltages add: V_supply = V₁ + V₂ + … (Kirchhoff’s voltage law).
• Voltage across one resistor: V_n = I × R_n, or by divider rule V_n = V_supply × (R_n / R_total).

Worked example 1 — series total. 10 Ω, 22 Ω, and 68 Ω in series:

R_t = 10 + 22 + 68 = 100 Ω.

At 28 V across the string: I = 28 / 100 = 0.28 A. Drop on 68 Ω: V = 0.28 × 68 = 19.04 V.

Worked example 2 — divider. Two series resistors 3 kΩ and 1 kΩ across 28 V. Voltage across 1 kΩ:

V = 28 × (1 / 4) = 7 V. Across 3 kΩ: 21 V. Same current I = 28 / 4000 = 7 mA.

Parallel Resistors

For resistors in parallel (same two nodes across each):

1 / R_eq = 1/R₁ + 1/R₂ + 1/R₃ + …

Special cases:

• Two resistors: R_eq = (R₁ R₂) / (R₁ + R₂) (product over sum).
• n equal resistors of value R: R_eq = R / n.
• R_eq is always less than the smallest individual parallel resistor.

Properties:

• Same voltage across every parallel branch.
• Currents add: I_total = I₁ + I₂ + … (Kirchhoff’s current law).
• Branch current I_n = V / R_n.

Worked example 3 — two parallel. 60 Ω ∥ 30 Ω:

R_eq = (60 × 30) / (60 + 30) = 1800 / 90 = 20 Ω.

Across 12 V: I_total = 12 / 20 = 0.6 A; through 30 Ω: 12/30 = 0.4 A; through 60 Ω: 0.2 A.

Worked example 4 — three equals. Three 150 Ω in parallel → R_eq = 150 / 3 = 50 Ω.

Series–Parallel Combinations

Exam networks rarely stay pure series or pure parallel. Reduce innermost groups first.

Worked example 5 — classic ladder. R₁ = 10 Ω in series with the parallel combination of R₂ = 40 Ω and R₃ = 40 Ω, all across 30 V.

1. Parallel pair: 40 ∥ 40 = 20 Ω.
2. Series with 10 Ω: R_eq = 10 + 20 = 30 Ω.
3. Supply current I = 30 / 30 = 1.0 A.
4. Drop on 10 Ω: 1.0 × 10 = 10 V; remaining 20 V across the parallel pair.
5. Each 40 Ω branch: I = 20 / 40 = 0.5 A (currents sum to 1.0 A).

Worked example 6 — aircraft lamp bank idea. Two 28 V lamps modelled as 14 Ω each in parallel, fed through a 1 Ω harness resistance from a 28 V bus.

• Lamp pair: 14 ∥ 14 = 7 Ω.
• Total: 1 + 7 = 8 Ω.
• I_bus = 28 / 8 = 3.5 A.
• Harness drop = 3.5 × 1 = 3.5 V; lamps see 24.5 V — a concrete reminder that wiring resistance is part of the series network.

Potentiometers

A potentiometer (“pot”) is a three-terminal variable resistor:

• Two ends of a resistive track (or wound element).
• A movable wiper contacting the track.

Operation

Connected as a voltage divider: end terminals across a reference voltage; wiper taps a fraction of that voltage. Ideal unloaded wiper voltage:

V_wiper ≈ V_ref × (R_bottom / R_total)

where R_bottom is the resistance between wiper and the reference return end.

Typical uses

• Panel brightness / volume / gain controls (training and avionics analogues).
• Adjustable set-points and calibration trimmers (preset pots).
• Sensor scaling when a stable reference voltage must be subdivided.

Construction notes

• Carbon track, cermet, or wirewound elements.
• Rotary or linear slide mechanics.
• Power rating of the track matters if significant current flows end-to-end or through the wiper.
• Loading the wiper with a low resistance alters the ideal divider ratio — Module 3 may expect qualitative awareness that a pot assumes a relatively light load on the wiper.

Rheostats

A rheostat is a variable resistor used primarily to control current in a circuit. Electrically it is often the same component family as a potentiometer but wired with two terminals: one end of the track plus the wiper (the unused end may be tied to the wiper for reliability).

Operation

Series rheostat with a load:

I = V / (R_rheostat + R_load)

Increasing inserted R lowers current (and power in the load, for a fixed supply).

Typical uses

• Laboratory current adjustment.
• Older lamp dimming / heater control concepts in training syllabi.
• Motor field or similar adjustment illustrations (principles level on Module 3).

Construction

Often wirewound for higher current. Larger physical size than signal pots when wattage is high — same I²R reality as fixed power resistors.

Potentiometer vs Rheostat Comparison

Key exam trap: Calling every variable resistor a “rheostat” when the stem shows three terminals across a supply with a wiper output — that is potentiometer (divider) operation. Conversely, a two-terminal variable R in series with a lamp is rheostat operation even if the part was manufactured as a pot.

Limitations Shared by Variable Resistors

• Wiper noise / wear after cycling — intermittent contact.
• Resolution limited by wire turns (wirewound) or track grain.
• Power concentrated in the portion of track carrying current.
• Temperature drift of the track resistance (link to §6.1 / §6.4).
• Not a precision voltage reference by themselves — they divide whatever reference you give them.

Exam Scenario Mindset

Reduce networks methodically, quote whether current or voltage is common, then classify the variable device by connection, not by the word stamped on the schematic alone. Series/parallel fluency plus pot-versus-rheostat vocabulary is exactly what topic 3.7 combination items test.