Find the resistance that must be placed in series with a \({\rm{25}}{\rm{.0}}\;{\rm{\Omega }}\) galvanometer having a \({\rm{50}}{\rm{.0}}\;{\rm{\mu A}}\) sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a \({\rm{0}}{\rm{.100}}\;{\rm{V}}\) full-scale reading.

A galvanometer is an electric current measurement device that can be used as both a voltmeter and ammeter. If we connect a high resistance in series with the galvanometer, it acts as a voltmeter and when a low resistance is connected in parallel, it acts as an ammeter.

• Inner resistance in galvanometer:\({\rm{25}}{\rm{.0}}\;{\rm{\Omega }}\)
• Sensitivity of galvanometer:\({\rm{50}}{\rm{.0}}\;{\rm{\mu A}}\)
• Scale measure of voltmeter: \({\rm{0}}{\rm{.100}}\;{\rm{V}}\)

The additional resistance\(R\)necessary for the galvanometer to have a\(V = 0.1\;{\rm{V}}\)full-scale reading, is given as-

\(\begin{array}{l}r + R = \frac{V}{I}\\R = \frac{V}{I} - r\\R = \frac{{{\rm{0}}{\rm{.1}}\;{\rm{V}}}}{{{\rm{50 \mu A}}}} - 25 \Omega \\R = 1975 \Omega \end{array}\)

The total resistance in this case is\(r + R\).

Therefore, the value for resistance is obtained as \(R = 1975 \Omega \).