Three voltmeters A , B and C having resistances R, 1.5 R and 3R respectively are used in a cirrcuit 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) ltV_(2)=V_(3)`
C. `V_(1)gtV_(2)gtV_(3)`
D. `V_(1)gtV_(2)=V_(3)`

Answer

A

Explanation

Here,` V_(2)=V_(3)`

i.e. `i_(2)xx1.5R=3Rxxi_(3)`
`and i_(2)+i_(3)=i`
`impliesi_(2)=(2i)/(3)and i_(3)=(i)/(3)`
Now, `V_(i)=iR`
`V_(2)=(2i)/(3)xx1.5R=iR`
`V_(3)=i/3xx3R=iR`
i.e. `V_(1)=V_(2)=V_(3)`