# Faulty voltmeter problem

## Homework Statement

A person measures 9volts accross the battery, 3 volts accross the resistor Ra and 4.5volts accross the resistor Rb connected in series (all three battery, Ra, Rb are connected in series) with a voltmeter of finite resistance. The resistor Ra=2M, and the battery has negligible internal resistance. Find- 1.The resistor Rb and 2. The internal resistance of the voltmeter.

[M=mega ohms]

## Homework Equations

- Ohm's law and Kirchoff's laws are only possible relevant equations.

## The Attempt at a Solution

- I really didnot get this. Shouldnt the voltages at the two resistors add up to give battery voltage?

[source of the question- tifr gs 2010]

CWatters
Homework Helper
Gold Member
The voltages across each resistor should add up to the battery voltage BUT only if the impedance of the voltmeter is very high. If the impedance of the voltmeter isn't very high (compared to the circuit impedance) then the volt meter will behave like an additional resistor that loads up the circuit and messes with the voltages. Note that it's not just the displayed voltage, it's the actual voltage that's affected. In some cases a circuit might work fine until you attach a voltmeter and then it stops working! Same applies to scope probes.

Pretend the voltmeter in the problem is an ideal meter in parallel with an unknown resistor. The resistor represents the input impedance of the real world meter.

CWatters
Homework Helper
Gold Member
For info...

Modern digital multimeters typically use an input amplifier based on a FET transistor or similar to ensure the input impedance is very high. I have one with an input impedance of 10MOhms.

When my father started out an engineer such things didn't exist. Voltmeters were just moving coils of wire and they might have an imput impedance of just 1,000 ohms. Every time you tried to measure a voltage you had to correct for the loading effect of the meter exactly as per this problem.