Chapter 19, Problem 57P

To determine

The sensitivity of the voltmeter.

Answer to Problem 57P

The sensitivity of the voltmeter is $100\Omega /\text{V}$ .

Explanation of Solution

Given info:

The reading of the millimeter is, $I=10\text{mA}=1\times {10}^{-2}\text{A}$ .

The resistance of the galvanometer is, $R=33\Omega$ .

The resistance in parallel with galvanometer is, $r=0.20\Omega$ .

The full scale reading of the voltmeter is, $V=10\text{V}$ .

Formula Used:

The expression to calculate the sensitivity of voltmeter is,

  $s=\frac{\frac{V}{I}-\frac{1}{\left(\frac{1}{R}+\frac{1}{r}\right)}}{V}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}R=\frac{\frac{10\text{V}}{1\times {10}^{-2}\text{A}}-\frac{1}{\left(\frac{1}{30\Omega }+\frac{1}{0.2\Omega }\right)}}{10\text{V}}\\ =100\Omega /\text{V}\end{array}$

Conclusion:

Thus, the sensitivity of the voltmeter is $100\Omega /\text{V}$ .