Question

What is the resistance of an ideal voltmeter?

Answer 1

When we place a voltmeter in a circuit, it draws a small current from the circuit, resulting in a lower measured voltage on the test point than without the voltmeter connected. For a voltmeter to become ideal, it must not influence the circuit it is measuring. The idea of an ideal voltmeter is only a theoretical concept.

Complete step by step answer:
Now, let us look at how we can construct an ideal voltmeter and how it could function when it is connected to a circuit. A voltmeter is connected to a circuit for measuring the potential difference between two points. So, it is always connected parallel to the wire carrying current.
So, we know that if an apparatus is connected to a circuit carrying current and it conducting, then a finite amount of current will pass through it. So, this will change the actual flow of current and hence the potential difference between two points.
This is the point where we think of an ideal voltmeter. If we need to minimize this drop, we must make the current passing through the voltmeter to minimum. Therefore we will keep the resistance of the voltmeter as high as possible (infinity for ideal case).
So, we can conclude that in an ideal situation, when the voltmeter is able to measure actual potential difference across two points, there should be no current passing through it and hence its resistance should be infinite.

Here,${{R}_{in}}=\infty$for an ideal voltmeter.

Note:
So, know we know what the resistance of an ideal voltmeter is. But, if we use zero or finite resistance, the voltmeter will draw all or significant amounts of current from the circuit and hence there will be a huge difference in actual value and measured value. We must be aware that there is no such real ideal voltmeter, it is only a theoretical concept.