A voltmeter has a range `O - V` with a series resistance `R`. With a series resistance `2R`, the range is `O - V`. The correct relation between `V` and `V'`is

Options

A. `V' lt 2V`
B. `V' gt 2V`
C. `V'=2V`
D. `V'=V`

Answer

A

Explanation

Let G be the resistance of voltmeter. Then for 0 - V range,
`I_(g)=(V)/(R+G) " " ` …(i)
and for 0 - V' range,
`I_(g)=(V')/(2R+G) " " ` …(ii)
Equating Eqs. (i) and (ii), we get
`(V)/(R+G)=(V')/(2R+G)`
`therefore (V')/(V)=(2R+G)/(R+G)=(2(R+G)-G)/(R+G)`
`=2-(G)/(R+G) lt 2 or V' lt 2V`