Calculating Mean Square Value of a Thermoelectric Ammeter Circuit

Click For Summary
SUMMARY

The discussion focuses on calculating the mean square value of a thermoelectric ammeter circuit, specifically addressing the integration limits for periodic signals. It clarifies that the integral can be taken from 0 to T, as long as it encompasses one complete cycle of the waveform. The final mean square value may differ from i² due to the presence of additional harmonics in the waveform, such as a sine wave combined with its second harmonic. Understanding these principles is crucial for accurate measurements in alternating current (AC) circuits.

PREREQUISITES
  • Understanding of thermoelectric ammeter operation
  • Knowledge of periodic signals and their properties
  • Familiarity with RMS (Root Mean Square) calculations
  • Basic principles of harmonic analysis in waveforms
NEXT STEPS
  • Study the derivation of RMS values for different waveforms
  • Learn about harmonic distortion and its effects on AC measurements
  • Explore the application of Fourier series in analyzing periodic signals
  • Investigate the characteristics of thermoelectric devices in electrical circuits
USEFUL FOR

Electrical engineers, students studying circuit theory, and professionals involved in AC measurement and analysis will benefit from this discussion.

MissP.25_5
Messages
329
Reaction score
0
I don't understand a few things here.

Firstly, here's the question:

This is thermoelectric ammeter. Internal resistance can be ignored.
1. Find the mean square value of the circuit.
2. Find the value that is displayed on the ammeter (alternating current).

In the textbook, the formula for the mean square value of a periodic signal is given -T/2 to T/2 as the integral region but here in the answer given, it's from 0 to T. Why?

And how come the final answer for number 1 differs from i^2?
 

Attachments

  • IMG_5854.jpg
    IMG_5854.jpg
    30.7 KB · Views: 501
  • IMG_5855.jpg
    IMG_5855.jpg
    34.6 KB · Views: 531
Last edited:
Physics news on Phys.org
Hi MissP. It doesn't matter what the region is, so long as it covers one complete cycle of the periodic waveform. You can choose whatever end-points you like, or just whatever is convenient. The average over any duration of T will be the same, wherever you choose as the starting point. (If it isn't, then it's not a periodic wave.)

I'm guessing that you are determining the RMS value of a wave comprising a sine wave plus some of its second harmonic?
 

Similar threads

Engineering Voltmeter and ammeter calculation in a circuit
  • · Replies 6 ·
Replies
6
Views
5K
Engineering Calculating the effective value and frequency of AC Circuit
  • · Replies 2 ·
Replies
2
Views
2K
How to determine drain-source voltage for this MOSFET amplifier.
  • · Replies 0 ·
Replies
0
Views
2K
Reading of Ammeter for this circuit with Voltage Controlled Resistors
  • · Replies 9 ·
Replies
9
Views
1K
Measurement technology textbook problems
  • · Replies 2 ·
Replies
2
Views
759
Measurement technology textbook problems
  • · Replies 1 ·
Replies
1
Views
841
Engineering Reconstruct a signal by determining the N Fourier Coefficients
  • · Replies 6 ·
Replies
6
Views
5K
Help me understand how this breadboard works?
  • · Replies 6 ·
Replies
6
Views
2K
Reading of a voltmeter and an ammeter
  • · Replies 4 ·
Replies
4
Views
4K
Lab Experiment: Estimate the error in these measurements of Ohm's law
  • · Replies 2 ·
Replies
2
Views
3K