Question

Three voltmeters f, B and C having resistances $R, 1.5 R$ 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 $V_1 V_2$ 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. $V_{1}>V_{2}=V_{3}$

Answer 1

Answer: (A)

Here, $V_{2}=V_{3}$
i.e. $i_{2} \times 1.5 R=3 R \times i_{3}$ and $i_{2}+i_{3}=i$
$\Rightarrow \, i_{2}=\frac{2 i}{3}$ and $i_{3}=\frac{i}{3}$
Now, $V_{1}=i R$
$V_{2}=\frac{2 i}{3} \times 1.5 R=i R$
and $V_{3}=\frac{i}{3} \times 3 R=i R$
i.e. $V_{1}=V_{2}=V_{3}$