Three voltmeters A, B and C having resistances R, 1.5 R and 3 R respectively are used in a circuit as shown. When a potential difference is applied between X and Y, the readings of the voltmeters are `V_1, V_2 and V_3 `respectively. Then :

Options

A. `V_(1)=V_(2)=V_(3)`
B. `V_(1) lt V_(2)=V_(3)`
C. `V_(1) gt V_(2) gt V_(3)`
D. `V_(1) gt V_(2)=V_(3)`

Answer

A

Explanation

Here, `V_(2)=V_(3)`
i.e. `i_(2) xx 1.5 R =3R xx i_(3) and i_(2)+i_(3)=i`
`rArr i_(2)=(2i)/(3) and i_(3)=(i)/(3)`

Now, `V_(1)=iR`
`V_(2)=(2i)/(3) xx 1.5R=iR`
and `V_(3)=(i)/(3) xx 3R=iR` i.e. `V_(1)=V_(2)=V_(3)`