Question

In the circuit shown in the figure, resistors $X$ and $Y$, each with resistance $R$, are connected to a $6\text{V}$ battery of negligible internal resistance. A voltmeter, also of resistance $R$, is connected across $Y$.


What is the reading of the voltmeter ?

• A. zero
• B. between $0$ and $3\text{V}$
• C. $3\text{V}$
• D. between $3\text{V}$ and $6\text{V}$

Answer 1

The correct option is B between $0$ and $3\text{V}$

The circuit may be redrawn as



From the diagram, current is given by

$I=\frac{6}{3R/2}=\frac{4}{R}$

Therefore, current through the voltmeter is $I/2$ or $2/R$.

So, the reading of the voltmeter is given by

$V=\frac{I}{2}\times R=\frac{2}{R}\times R=2\text{V}$

Hence, option $\left(b\right)$ is correct.
$$\begin{array}{c}\text{Why this question?}\\ \text{If the resistance of voltmeter is comparable}\\ \text{with the resistances of the circuit, then}\\ \text{it will affect the current in the circuit.}\\ \text{Ideally resistance of voltmeter is infinity.}\end{array}$$