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A voltmeter has a resistance of G ohm an...

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

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With a voltmeter of range V volt, the current i is given by
`i=(V)/(G)ldots(i)`
To change it into voltmeter of range av volt, the necessary series resistance be R. Then`i=(lambdaV)/(R+G)ldots(ii)
Equating equations (i) and (ii) `(V)/(G)=(lambdaV)/(R+G)`
It gives `R = (lambda - 1)G`
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