Q. Three voltmeters A, B and C having resistances R, 1.5R 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) $V_{1} = V_{2} = V_{3}$
B) $V_{1} < V_{2} = V_{2}$
C) $V_{1} > V_{2} > V_{3}$
D) $V_{1} > V_{2} > V_{3}$
Explanation
(a) Here, $V_{2} = V_{3}$
$ie.,\ i_{2} \times 1.5R = 3R \times i_{3}$
And $i_{2} + i_{3} = i$
$\Longrightarrow \ \ i_{2} = \frac{2i}{3}\ and\ i_{3} = \frac{i}{3}$
Now, $V_{i} = iR$
$\ \ \ \ \ \ \ \ \ V_{2} = \frac{2i}{3} \times 1.5R = iR$
$\ \ \ \ \ \ \ \ V_{3} = \frac{i}{3} \times 3R = iR$
$ie,\ \ \ \ \ V_{1} = V_{2} = V_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.