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

Answer

D

Explanation

`V = (R + G)i_(g)`
`V^(.) =(2R + G)i_(g)`
`rArr V/V^(.) =(R + G)/(2R + G) rArr V^(.)/V =(2(R +G)-G)/(R + G)`
`= 2- G/(R +G)`
`rArr V^(.) = 2V - (GV)/(R + G)`
`rArr V. lt 2V`