Calculating Mean Square Value of a Thermoelectric Ammeter Circuit

In summary, the conversation discusses finding the mean square value and displayed value on a thermoelectric ammeter, with a question about the integration region and the difference between the final answer and i^2. The answer is that the integration region can be chosen arbitrarily as long as it covers one complete cycle, and the average over any duration of T will be the same for a periodic wave. The questioner is also determining the RMS value of a wave that includes a sine wave and its second harmonic.
  • #1
MissP.25_5
331
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?
 

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  • #2
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?
 

1. How is the mean square value of a thermoelectric ammeter circuit calculated?

The mean square value of a thermoelectric ammeter circuit is calculated by taking the square of each individual value measured by the ammeter and then finding the average of these squared values.

2. What is the purpose of calculating the mean square value of a thermoelectric ammeter circuit?

The mean square value of a thermoelectric ammeter circuit is used to determine the average power dissipated by the circuit. This information is important for monitoring and optimizing the performance of the circuit.

3. Can the mean square value be calculated from a single measurement?

No, the mean square value requires multiple measurements to be taken and then averaged. A single measurement would not provide an accurate representation of the overall power dissipation in the circuit.

4. What factors can affect the accuracy of the mean square value calculation?

The accuracy of the mean square value calculation can be affected by factors such as fluctuations in the temperature or voltage of the circuit, as well as errors in the ammeter readings.

5. Are there any alternative methods for calculating the mean square value of a thermoelectric ammeter circuit?

Yes, there are alternative methods such as using a digital multimeter to directly measure the power dissipation of the circuit or using computer simulations to calculate the mean square value. However, the traditional method of squaring and averaging individual measurements is still commonly used and is considered accurate.

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