The correct principle on which a Resistance Temperature Detector (RTD) works is that the resistance increases with an increase in temperature. This can be explained in the following way:

1. Basic Principle of RTD: An RTD measures temperature by correlating the resistance of the RTD element with temperature. Metals have a positive temperature coefficient of resistance, meaning their resistance increases with an increase in temperature.
2. Material Used: The most common metals used in RTDs are platinum, nickel, and copper. Platinum is widely used due to its stable and reproducible resistance-temperature relationship.
3. Resistance-Temperature Relationship: The resistance of an RTD changes approximately linearly with temperature, which can be mathematically expressed using the formula: \(R_t = R_0 (1 + \alpha \Delta T)\)
   • \(R_t\) is the resistance at temperature \(T\).
   • \(R_0\) is the resistance at a reference temperature (usually 0°C).
   • \(\alpha\) is the temperature coefficient of resistance specific to the material used in the RTD.
4. Comparison with Options:
   • Option 1: "Resistance increases with increase in temperature" is correct as RTDs work on this principle.
   • Option 2: "Resistance remains constant with temperature" is incorrect because the resistance varies with temperature in an RTD.
   • Option 3: "Resistance decreases with increase in temperature" is incorrect as this would contradict the principle of operation of RTDs.
   • Option 4: "Voltage decreases with increase in temperature" is unrelated to the working principle of an RTD, which involves resistance changes, not voltage changes.

Thus, the principle that fits best in the context of RTDs is that the resistance increases with an increase in temperature.