question_answer

Three voltmeters A, B and C having resistances R, 1.5R 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 \[{{V}_{1}},\text{ }{{V}_{2}}\], and \[{{V}_{3}}\]respectively. Then

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

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