Question

Unlike the idealized voltmeter, a real voltmeter has a resistance that is not infinitely large.

A voltmeter with resistance RV is connected across the terminals of a battery of emf E and internal resistance r. Find the potential difference Vmeter measured by the voltmeter.

What is Vmeter?

Answer 1

Concepts and reason

The concepts used to solve this problem are Kirchhoff’s loop rule and ohm’s law.

Initially, the current flowing through the circuit can be calculated by using the Kirchhoff’s loop rule.

Finally, potential difference of the voltmeter can be calculated by using the ohm’s law for the circuit.

Fundamentals

Kirchhoff’s loop rule states that the sum of voltage across the all the circuit elements will be equal to zero.

The circuit diagram for the voltmeter is,

Applying the Kirchhoff’s loop rule, the equation will be,

Here, is the battery emf, is the current flowing through the circuit, is the voltmeter resistance, and is the internal resistance.

The expression for the potential difference of the voltmeter by applying Ohm’s law is,

Here, is the potential difference of the voltmeter.

According to the Kirchhoff’s loop rule, the equation will be,

Rewrite the above equation to find the current flow through the circuit.

The expression for the potential difference of the voltmeter is,

Substitute for .

Ans:

The required potential difference measured by the voltmeter is .