What is the change in resistance of a Voltemter if its range is increases by n times ?

Explanation

A galganometer has range `I_(g)` and resistance G. when used as a voltmeter itr range `V_(G)=I_(G)*G`.
Resistance to be connected in series withG to convete it into a voltmeter of range V is,
`R=(V)/(I_(G))-G=G((V)/(V_(G)*G)-1)=G((V)/(V_(G))-1)`
`=G(n-1)[ :. (V)/(V_(G))=n]`
Now, the equivalent resistance of the series combination of g and `R,G+R=G+G(n-1)=nG`.
So, when range of voltmeter is n times its reistance becomes n time.