Question

A resistance potentiometer has a total resistance of $10000\ \Omega$ and is rated $4\text{ W}$. If the range of the potentiometer is $0$ to $100\text{ mm}$, then its sensitivity in $\text{V/mm}$ is:

• A. 1.0
• B. 2.0
• C. 2.5
• D. 25

Hint:

Potentiometer sensitivity is directly proportional to its maximum applied voltage.
Always use the power dissipation formula $P = V^2/R$ to find this maximum voltage limit first.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the sensitivity of a linear resistance potentiometer.
We are given its total resistance, power rating, and maximum displacement range.

Step 2: Key Formula or Approach:
The maximum excitation voltage $V_{max}$ that can be applied across the potentiometer is determined by its power rating $P$ and resistance $R$:
\[ P = \frac{V_{max}^2}{R} \implies V_{max} = \sqrt{P \cdot R} \]
The sensitivity $S$ of the potentiometer is the change in output voltage per unit change in input displacement:
\[ S = \frac{V_{max}}{x_{max}} \]

Step 3: Detailed Explanation:

• Given parameters:
Total resistance, $R = 10000\ \Omega$.
Power rating, $P = 4\text{ W}$.
Maximum displacement range, $x_{max} = 100\text{ mm}$.

• Calculate the maximum safe operating voltage $V_{max}$:
\[ V_{max} = \sqrt{4 \times 10000} = \sqrt{40000} = 200\text{ V} \]

• Calculate the sensitivity $S$:
\[ S = \frac{200\text{ V}}{100\text{ mm}} = 2.0\text{ V/mm} \]

Step 4: Final Answer:
The sensitivity of the potentiometer is $2.0\text{ V/mm}$, which corresponds to Option (B).