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 V1 V2 and V3, respectively then.

Question

(A) V1=V2=V3 (B) V1< V2=V3 (C) V1>V2>V3 (D) V1>V2=V3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/33e78b59acb1264ccb2c939ea27d9cb1-.png" /> Here, V2=V3 i.e. i2 × 1.5 R=3 R × i3 and i2+i3=i ⇒ i2=(2 i/3) and i3=(i/3) Now, V1=i R V2=(2 i/3) × 1.5 R=i R and V3=(i/3) × 3 R=i R i.e. V1=V2=V3

Q. 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.

$V_{1} = V_{2} = V_{3}$

$V_{1} < V_{2} = V_{3}$

$V_{1} > V_{2} > V_{3}$

$V_{1} > V_{2} = V_{3}$

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. $V_{1} = V_{2} = V_{3}$

Q. Three voltmeters f, 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 V1​V2​ and V3​, respectively then.

V1​=V2​=V3​

V1​<V2​=V3​

V1​>V2​>V3​

V1​>V2​=V3​