Question

To reduce the range of voltmeter, its resistance needs to be reduced. A voltmeter has resistance \[{{R}_{0}}\] and range \[V\]. Which of the resistances when connected in parallel will convert it into a voltmeter of range \[V/n\]?
\[\begin{align}
  & A)n{{R}_{0}} \\
 & B)\left( n+1 \right){{R}_{0}} \\
 & C)\left( n-1 \right){{R}_{0}} \\
\end{align}\]
\[D)\] none of these.

Answer 1

Hint: If we connect two resistance in parallel and connect to a source of voltage, the voltage through each branch will be the same. If we connect these two resistances in series, the current through each of them will be the same and voltage will be different according to ohm’s law. It is given that if we need to reduce the range of voltmeter, we need to reduce its resistance.

Complete step by step answer:
We know that voltmeter works on the principle of ohm’s law, which states that the voltage across a resistance is directly proportional to the current passing through it. A voltmeter is always connected parallel to the points where the potential is needed to be found.
Now, as per the question, if we connect a resistance parallel to a voltmeter to reduce its range, it will not reduce its range but the combination of resistance will be reduced. This is because there will be internal resistance of \[{{R}_{0}}\] already and if we connect another resistance parallel to it, it will reduce the combined resistance but the range will remain the same.
So, we can conclude that the range of a voltmeter cannot be reduced by connecting a parallel resistance to it.

Therefore option d is the correct answer.

Note:
If we need to reduce the range of a voltmeter, a resistance must be connected in series. But we must know that this couldn’t be achieved by connecting a resistance in parallel. We should note that the range of a voltmeter can only be increased but cannot be reduced.