question_answer

A voltmeter has resistance of G ohm and range of V volt. The value of resistance used in series to convert it into a voltmeter of range nV volt is:

A)  \[n\,\,\,G\]          

B)  \[(n-1)\,\,G\]

C)  \[\frac{G}{n}\]

D)  \[\frac{G}{n-1}\]

Correct Answer: B

Solution :

 Let G is resistance of galvanometer and \[{{i}_{g}}\] the current through it. From Ohms law \[{{i}_{g}}=\frac{V}{G+R}\] \[\Rightarrow \] \[G+R=\frac{V}{{{i}_{g}}}\] \[\Rightarrow \] \[R=\frac{V}{{{i}_{g}}}-G\] Given, \[V=n\,\,V,{{i}_{g}}=\frac{V}{G}\] \[\therefore \] \[R=\frac{n\,\,V}{V/G}-G=n\,G-G=(n-1)\,G\]