question_answer

A, B and C are voltmeters of resistance R, 1.5 R and 3R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are \[{{V}_{A}},{{V}_{B}}\] and \[{{V}_{C}}\] respectively.                                                                                                      [NEET  2015]

Then,

A)  \[{{V}_{A}}={{V}_{B}}={{V}_{C}}\]

B)       \[{{V}_{A}}\ne {{V}_{B}}={{V}_{C}}\]

C)  \[{{V}_{A}}={{V}_{B}}\ne {{V}_{C}}\]

D)                   \[{{V}_{A}}\ne {{V}_{B}}\ne {{V}_{C}}\]

Correct Answer: A

Solution :

[a] The equivalent resistance between Q and S is given by

\[\frac{1}{R'}=\frac{1}{1.5R}+\frac{1}{3R}=\frac{2+1}{3R}\]

\[\Rightarrow \]   \[R'=R\]

Now,     \[{{V}_{PQ}}={{V}_{A}}+IR\]

Also      \[{{V}_{QS}}={{V}_{B}}={{V}_{C}}=IR\]

Hence,  \[{{V}_{A}}={{V}_{B}}={{V}_{C}}\]