Resistance thermometers, also known as resistance temperature detectors (RTDs), are temperature sensors that rely on the measurement of resistance to determine the temperature. They are commonly used in various industries and applications due to their accuracy and stability.

The correct option for the measurement of resistance in a resistance thermometer is the Wheatstone bridge. Let's understand why this is the case.

Wheatstone Bridge:
A Wheatstone bridge is an electrical circuit that is widely used for measuring resistance. It consists of four resistive arms connected in a diamond shape, with a voltage source connected across two opposite corners and a galvanometer connected across the other two corners.

Working Principle:
When a known resistance (known as the reference resistor) is connected in one arm of the bridge and the resistance being measured (in this case, the resistance of the resistance thermometer) is connected in another arm, the bridge is said to be balanced when the galvanometer shows zero deflection.

At balance, the ratio of the two resistances is equal to the ratio of the other two resistances in the bridge. Mathematically, this can be expressed as:

R1/R2 = R3/R4

In the case of resistance thermometers, the reference resistor is a known resistance, and the resistance being measured is the resistance of the temperature sensor. As the temperature changes, the resistance of the sensor also changes, leading to an imbalance in the Wheatstone bridge.

Measurement Process:
To measure the resistance of the resistance thermometer, the Wheatstone bridge is adjusted to achieve balance by varying the value of a variable resistor in one of the arms. The resistance value can then be determined by measuring the position of the variable resistor.

Advantages of Wheatstone Bridge for Resistance Measurement:
1. High Accuracy: The Wheatstone bridge method offers high accuracy in measuring resistance, making it suitable for precise temperature measurements.
2. Wide Temperature Range: Resistance thermometers can measure a wide range of temperatures, and the Wheatstone bridge provides a reliable method for accurate measurement across this range.
3. Stability: Wheatstone bridge circuits are stable and not affected by external factors such as voltage fluctuations or changes in the supply.

In conclusion, resistance thermometers make use of the Wheatstone bridge for the measurement of resistance. This method offers high accuracy, stability, and is suitable for a wide range of temperature measurements.