Question

A, B, and C are voltmeters of resistance $R$, $1.5R$, and $3R$ respectively. When some potential difference is applied between $X$ and $Y$, the voltmeter readings are $V_A,V_B$, and $V_C$, respectively.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. $V_B\ne V_A=V_C$

Answer 1

The correct option is A $V_A=V_B=V_C$

Let $i$ be the total current through the circuit, as per KCL the current will be divided into two parts as shown in figure.
Now, the equations for the voltages across the three voltmeters are,
$V_A=iR$,
$V_B=\frac{2i}{3}\times 1.5R=iR$ and
$V_C=\frac{i}{3}\left(3R\right)=iR$
$\therefore V_A=V_B=V_C$