6.4 Wheatstone Bridge, Thermistors & Temperature Coefficient

6.4 Wheatstone Bridge, Thermistors & Temperature Coefficient

Quick Answer: A Wheatstone bridge balances when R₁/R₂ = R₃/R₄ (equivalently R₁ R₄ = R₂ R₃), so the mid-points are at equal potential. NTC thermistors fall in R as temperature rises; PTC rise in R as temperature rises. VDRs (varistors) change R with voltage. Know fixed vs variable resistor roles and limits.

Topic 3.7 finishes by connecting resistance to measurement and sensing. Bridges measure unknown resistance accurately; thermistors convert temperature to resistance; VDRs protect or sense based on voltage.

Wheatstone Bridge — Construction and Balance

A classical Wheatstone bridge has four resistive arms in a diamond (or rectangle) arrangement:

• Two voltage dividers share the same supply.
• A galvanometer or detector connects between the divider mid-points.

Label the arms so that one divider is R₁ (top) and R₂ (bottom), the other R₃ (top) and R₄ (bottom), with the meter between the junctions of R₁–R₂ and R₃–R₄. (Textbook lettering varies; learn the ratio condition, not one fragile letter pattern.)

Balance condition

At balance, detector current is zero and the two mid-point potentials are equal. Then:

R₁ / R₂ = R₃ / R₄

or

R₁ × R₄ = R₂ × R₃

If R₄ is the unknown and R₁, R₂, R₃ are known (R₃ often a calibrated variable):

R₄ = R₃ × (R₂ / R₁) — rearrange to match your diagram’s knowns.

Worked example 1 — balance check. R₁ = 100 Ω, R₂ = 100 Ω, R₃ = 470 Ω, R₄ = 470 Ω.

R₁/R₂ = 1 and R₃/R₄ = 1 → balanced. Galvanometer reads zero.

Worked example 2 — find unknown. Bridge balanced with R₁ = 1 kΩ, R₂ = 4 kΩ, R₃ = 2.5 kΩ. Find Rₓ in the R₄ position using R₁/R₂ = R₃/Rₓ.

1/4 = 2.5 / Rₓ → Rₓ = 2.5 × 4 = 10 kΩ.

Worked example 3 — off balance (qualitative). If R₄ increases above the balance value, one mid-point potential shifts and detector current flows in a definite direction — used in null methods and in some sensor bridges where imbalance voltage is the output (strain gauges, RTD bridges — principles level).

Why bridges appear on Module 3

• Accurate resistance measurement without relying only on a simple ohmmeter scale.
• Null (balance) methods can be highly sensitive.
• Links series/parallel divider ideas from §6.3 into a measurement instrument.

Temperature Coefficient Revisited

Temperature coefficient of resistance (α) quantifies how R changes with temperature. Section 6.1 used R_t = R₀[1 + α(Δt)] for approximately linear metallic behaviour.

Thermistors

A thermistor is a temperature-sensitive resistor, usually a semiconductor ceramic, with a large resistance change over a modest temperature span — far more sensitive than copper wire for the same ΔT.

NTC thermistors (Negative Temperature Coefficient)

• Resistance falls as temperature rises.
• Common for temperature measurement, inrush limiting (cold NTC starts high-R then falls), and compensation networks.

Worked idea: An NTC might be 10 kΩ at 25 °C and only a few kilohms at elevated bay temperature — a divider output voltage shifts measurably.

PTC thermistors (Positive Temperature Coefficient)

• Resistance rises as temperature rises (often sharply near a transition for switching PTCs).
• Used for over-temperature protection, self-resetting current limiting concepts, and heater regulation illustrations.

Thermistor limitations

• Non-linear R–T curve (especially NTC) — calibration tables or linearising circuits needed for precision.
• Self-heating: measurement current through the thermistor raises its own temperature and errors the reading if too large.
• Tolerance and ageing — interchangeability poorer than precision wirewound resistors unless matched.
• Limited power dissipation compared with large wirewound parts.

Aircraft training context: temperature probes and compensation networks in electronics bays are the practical cousins of the syllabus thermistor — Module 3 wants the NTC vs PTC definition and qualitative use, not a full air-data computer design.

VDRs — Voltage Dependent Resistors (Varistors)

A VDR (voltage-dependent resistor), often a varistor (for example metal-oxide varistor, MOV),

has resistance that falls sharply when voltage exceeds a threshold, clamping surges.

Uses: transient suppression across supplies and signal lines (principles). Limitation: energy rating; repeated or huge surges degrade the device. Do not confuse VDRs with thermistors: one responds primarily to voltage, the other to temperature.

Fixed vs Variable Resistor Types — Roles and Limits

Fixed resistors are chosen when the circuit needs a stable, known R (within tolerance and TCR). Variable devices are chosen when the circuit must be adjusted or must respond to an environmental quantity. Mixing the categories on an exam stem — for example treating a thermistor as a precision fixed 1% metal-film stand-in — is a common mistake.

Putting Chapter 6 Together

1. Geometry and material set baseline R (ρL/A, temperature).
2. Colour code and preferred values identify commercial fixed parts; wattage sets heat capability.
3. Series/parallel and pots/rheostats build and adjust networks.
4. Bridges measure R; thermistors and VDRs make R a sensor or protector.

Exam scenario — bridge with thermistor. One arm is an NTC. As bay temperature rises, NTC resistance falls, the bridge unbalances, and detector voltage indicates temperature — the same balance equation still defines the null point when you substitute the thermistor’s R at that temperature.

Exam scenario — PTC protection. A PTC in series with a load stays low-R when cool; on over-current/over-temperature it rises in R and throttles current.

Exam scenario — VDR across a DC bus. Normal 28 V operation sees high VDR resistance; a voltage spike drives the VDR into conduction to clamp the transient.

Master the balance ratio, the NTC/PTC definitions, and the fixed vs variable limitation table. That closes CAAS Module 3 topic 3.7 Resistance / resistor.