Why Do Voltmeter Readings Differ in a Series Circuit?

  • Thread starter Thread starter swaha
  • Start date Start date
  • Tags Tags
    Voltmeter
AI Thread Summary
In a series circuit with a battery and two resistors, the voltmeter readings can differ due to the finite resistance of the voltmeter itself. When measuring voltages across resistors, if the voltmeter's impedance is not significantly higher than the circuit's impedance, it can load the circuit, affecting the voltage readings. This loading effect can lead to discrepancies, as the voltages across the resistors may not sum to the battery voltage. Modern digital multimeters have high input impedances, typically around 10M ohms, minimizing this effect compared to older analog voltmeters. Understanding the impact of voltmeter impedance is crucial for accurate voltage measurements in circuit analysis.
swaha
Messages
5
Reaction score
0

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]
 
Physics news on Phys.org
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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

Similar threads

Back
Top