Why Do Voltmeter Readings Differ in a Series Circuit?

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Homework Help Overview

The discussion revolves around a series circuit involving a battery and two resistors, where voltmeter readings across the components do not sum to the expected battery voltage. The subject area includes concepts from electrical circuits, specifically focusing on voltage measurements and the impact of voltmeter resistance.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster questions why the voltages across the resistors do not add up to the battery voltage, suggesting a misunderstanding of the circuit behavior. Some participants explain that the voltmeter's impedance affects the readings, introducing the concept of loading effects in measurements.

Discussion Status

Participants are exploring the implications of voltmeter resistance on voltage readings. There is acknowledgment of the differences in voltmeter technology over time, with some guidance provided regarding the behavior of modern digital multimeters compared to older models.

Contextual Notes

The problem context includes the specific values of resistors and the battery voltage, as well as the mention of the voltmeter's finite resistance, which is central to the discussion. The original poster's reference to a specific source indicates a homework constraint.

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Homework Statement


A person measures 9volts across the battery, 3 volts across the resistor Ra and 4.5volts across 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]
 
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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.
 
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.

See also..

http://en.wikipedia.org/wiki/Multimeter#Analog_multimeters
 
okay thanks.
 

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