Question

In a Voltmeter the sensitivity is given by:

• A. \( \Omega/\text{V} \)
• B. \( \text{V}/\Omega \)
• C. \( \text{A}/\text{V} \)
• D. \( \text{W}/\text{V} \)

Hint:

A higher \( \Omega/\text{V} \) rating is always desired in a voltmeter.
It implies that the instrument has a high internal resistance and will provide a more accurate voltage reading.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the mathematical unit and definition of sensitivity in an analogue voltmeter.
Voltmeter sensitivity is a key performance index that determines how much the instrument loads down the circuit under test.

Step 2: Key Formula or Approach:
By definition, voltmeter sensitivity (\( S \)) is the reciprocal of the full-scale deflection current (\( I_{\text{fsd}} \)) of the basic d'Arsonval movement:
\[ S = \frac{1}{I_{\text{fsd}}} \] Since Current \( I \) is measured in Amperes (\( \text{A} \)), and by Ohm's Law \( 1\text{ A} = \frac{1\text{ V}}{1\ \Omega} \), we can substitute the unit:
\[ [S] = \frac{1}{\text{Amperes}} = \frac{1}{\text{Volts}/\text{Ohms}} = \frac{\text{Ohms}}{\text{Volts}} = \Omega/\text{V} \]

Step 3: Detailed Explanation:
Let us look at the practical significance of this parameter:

• Internal Resistance Calculation:
The total internal resistance (\( R_v \)) of a voltmeter for a given voltage range \( V \) is computed as:
\[ R_v = S \times V \] For example, if a voltmeter has a sensitivity of \( 20,000\ \Omega/\text{V} \) and is set to the \( 100\text{ V} \) range, its total internal resistance is:
\[ R_v = 20,000 \times 100 = 2\ \text{M}\Omega \]
• Loading Effect: A higher sensitivity value implies a lower full-scale current requirement.
Consequently, a highly sensitive voltmeter will have a larger internal resistance and will draw less current from the circuit, reducing the loading error during measurements.

Step 4: Final Answer:
The sensitivity of a voltmeter is expressed in \( \Omega/\text{V} \).