question_answer

Three voltmeters A, B and C having resistances R, 1.5 R and \[3R\]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

A) \[{{V}_{1}}=\text{ }{{V}_{2}}=\text{ }{{V}_{3}}\]

B)  \[{{V}_{1}}<{{V}_{2}}={{V}_{3}}\]

C)  \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]

D)  \[{{V}_{1}}>{{V}_{2}}={{V}_{3}}\]

Correct Answer: A

Solution :

Here,             \[{{V}_{2}}={{V}_{3}}\] ie,         \[{{i}_{2}}\times 1.5R=3R\times {{i}_{3}}\] and          \[{{i}_{2}}+{{i}_{3}}=i\] \[\Rightarrow \] \[{{i}_{2}}=\frac{2i}{3}\]and \[{{i}_{3}}=\frac{i}{3}\] Now,           \[{{V}_{1}}=IR\] \[{{V}_{2}}=\frac{2i}{3}\times 1.5R=iR\] \[{{V}_{3}}=\frac{i}{3}\times 3R=iR\] ie, \[{{V}_{1}}={{V}_{2}}={{V}_{3}}\]