Calculating Voltmeter Sensitivity

The question asks us to determine the sensitivity of a voltmeter based on how much its reading changes in response to a change in the input voltage it is measuring.

Sensitivity of an instrument is a measure of how much the output changes for a given change in the input. It is typically defined as the ratio of the change in output quantity to the change in input quantity that causes it.

Understanding Instrument Sensitivity

For a measuring instrument like a voltmeter, the sensitivity tells us how finely it can register changes in the voltage being measured. A higher sensitivity means a smaller change in input voltage will result in a noticeable change in the voltmeter's reading (output).

Formula for Sensitivity

The general formula for sensitivity (S) is given by:

S = \frac{\text{Change in Output}}{\text{Change in Input}}

In this specific case, for the voltmeter:

\text{Sensitivity} = \frac{\text{Change in Voltmeter Reading}}{\text{Change in Input Voltage}}

Applying the Given Values

From the question, we are given the following information:

• Change in voltmeter reading (Output change) = 0.18 V
• Change in input voltage (Input change) = 0.2 V

Now, we can substitute these values into the sensitivity formula:

\text{Sensitivity} = \frac{0.18\text{ V}}{0.2\text{ V}}

Step-by-Step Calculation of Sensitivity

Let's perform the calculation:

\text{Sensitivity} = \frac{0.18}{0.2}

To make the division easier, we can multiply the numerator and denominator by 100 to remove the decimal points:

\text{Sensitivity} = \frac{0.18 \times 100}{0.2 \times 100} = \frac{18}{20}

Now, simplify the fraction:

\text{Sensitivity} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}

Convert the fraction to a decimal:

\text{Sensitivity} = 0.9

The units cancel out (V/V), so sensitivity is a dimensionless quantity in this context, or it can be considered in terms of V/V, but typically stated as a numerical value.

Result

The calculated sensitivity of the voltmeter is 0.9.

Revision Table: Instrument Sensitivity Calculation

Additional Information: Voltmeter Characteristics

Besides sensitivity, other important characteristics of a voltmeter include:

• Accuracy: How close the measured value is to the true value. Often expressed as a percentage of full scale or reading.
• Precision: The degree of reproducibility of measurements. How close repeated measurements are to each other.
• Resolution: The smallest change in the input quantity that the instrument can detect.
• Range: The set of values of the input quantity that the instrument is designed to measure.
• Input Impedance: Ideally, a voltmeter should have very high input impedance so that it doesn't draw significant current from the circuit being measured, which could alter the voltage itself.

Sensitivity is a key performance indicator for any measuring instrument as it relates directly to how well it can respond to variations in the quantity being measured.