Find average and rms values of the waveform

In summary, the conversation is discussing how to determine the average and rms value of a waveform depicted in a given figure. The solution involves identifying one period of the repeating waveform and using the appropriate equations to calculate the mean and rms values. There is confusion about the time interval and equation for average value, but it is clarified that T = 3 because it covers one period of the waveform.
  • #1
DODGEVIPER13
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Homework Statement


The problem is located here http://www.chegg.com/homework-help/determine-average-rms-value-waveform-depicted-fig-1136-chapter-11-problem-26e-solution-9780073529578-exc


Homework Equations


Rms=sqrt(1/T∫ from 0 to T of i(t)^2 DT )
Average= couldn't find an equation in book??

The Attempt at a Solution


Ok so I did it on my own and I'm trying to figure out why in the solution that the person posted. Is i(t) only written for 3 time intervals 0<t<2, 2<t<3, and 3<t<5. Why is there not a 4th 5<t<6 where i(t) would equal -9 A. BTW this is the first part if it wasn't clear. Furthermore how is T=5 I would think it would be 2 as the square wave gets its maximum at -9 and it lasts for 2 and 3? Also what is the equation for average value of current? And more of the same on the second part of the problem why did they only do parts of the waveform?
 
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  • #2
Or is the solution incorrect
 
  • #3
here is my work
 

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  • #4
It's a repeating waveform. The average (or rms) over one cycle (period) is the same as over all periods. So you need to identify one period and work with that. Looks to me like the time interval from 0 to 3 would cover one period of the repeating signal (the interval from 3 to 6 is an exact repetition).

The mean is calculated in the same way that the mean is calculated for the rms, only the function isn't squared. That is,

$$mean = \frac{1}{T}\int_{t_o}^{t_f}i(t)dt$$
 
  • #5
ah so T=3 then because it covers the time from its minimum to its max.
 
  • #6
T = 3 because it covers one period of the waveform. A period is the repeating unit of the waveform.
 
  • #7
ok thanks
 

1. What is the difference between average and rms values of a waveform?

The average value of a waveform is the sum of all the values divided by the total number of values. It represents the overall magnitude of the waveform over a given period of time. The rms (root mean square) value, on the other hand, is the square root of the average of the squared values. It represents the effective magnitude of the waveform and is commonly used to measure power or energy.

2. How do you calculate the average value of a waveform?

To calculate the average value of a waveform, you need to add up all the values of the waveform over a given period of time and then divide the sum by the total number of values. For example, if you have a waveform with values of 1, 2, 3, and 4 over a period of 4 seconds, the average value would be (1+2+3+4)/4 = 2.5.

3. What is the formula for calculating the rms value of a waveform?

The formula for calculating the rms value of a waveform is:
Vrms = sqrt((1/T) * integral from 0 to T (V(t)^2) dt)
where T is the period of the waveform and V(t) is the instantaneous voltage at time t.

4. Can the average value of a waveform be negative?

Yes, the average value of a waveform can be negative. This can occur when the waveform has both positive and negative values that cancel each other out when averaged over a given period of time. For example, a sine wave with an equal number of positive and negative cycles will have an average value of 0.

5. Why is the rms value used to measure power or energy in a waveform?

The rms value is used to measure power or energy in a waveform because it takes into account both the magnitude and the duration of the waveform. This is important when working with alternating current (AC) circuits, where the voltage and current are constantly changing. The rms value provides a more accurate representation of the effective power or energy in the waveform compared to the average value.

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