Question

A resistance potentiometer is:

• A. Zero order element
• B. First order element
• C. Second order element
• D. Third order element

Hint:

- Zero-order systems: No energy storage elements (e.g., potentiometer, strain gauge).
- First-order systems: One energy storage element (e.g., thermometer, RC low-pass filter).
- Second-order systems: Two energy storage elements (e.g., mass-spring-damper, RLC circuit).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question asks for the system dynamic order of a resistance potentiometer, which is a common displacement transducer.

Step 2: Key Formula or Approach:
The order of a measurement system or element is determined by the order of the differential equation that describes its input-output relationship.

Step 3: Detailed Explanation:

• A resistance potentiometer translates a mechanical displacement input $x(t)$ into an electrical voltage output $V_{out}(t)$.

• The relationship is given by:
\[ V_{out}(t) = \left( \frac{V_{ex}}{L} \right) x(t) \]
where $V_{ex}$ is the excitation voltage and $L$ is the total length of the potentiometer.

• In this equation, there are no derivative terms with respect to time (no $d/dt$ or $d^2/dt^2$ terms).

• The output responds instantaneously to changes in the input without any dynamic time delay or lag.

• Therefore, the system is represented by a zero-order algebraic equation, making it a zero-order instrument.

Step 4: Final Answer:
A resistance potentiometer is a zero-order element, corresponding to Option (A).