Calculating RMS Value of i=1/3sin3t

In summary, the formula for calculating the RMS value of i=1/3sin3t is (1/√2) x (1/3sin3t). This calculation is significant in determining the average power of an alternating current or voltage signal and comparing different signals. To calculate the RMS value, the function i=1/3sin3t should be squared, integrated over one period, divided by the period, and then multiplied by 1/√2. The units of the RMS value depend on the original units of the function, and it is equal to the peak value (amplitude) multiplied by 1/√2.
  • #1
robbieharibo
1
0
1. find the rms value of i=1/3sin3t between t=0 and t=1/10



2. not sure of the method or the formula i may need



3. Any help appreciated
 
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  • #2
For continuous functions the RMS over a time interval is

[tex] \sqrt{ \frac{1}{T_2 - T_1} \int_{T_1}^{T_2} [f(t)]^2 dt [/tex]
 
  • #3
robbieharibo said:
1. find the rms value of i=1/3sin3t between t=0 and t=1/10



2. not sure of the method or the formula i may need



3. Any help appreciated


rms is root mean squared

[tex]

V_{rms} = \sqrt{\frac{1} {(t_1-t_0)}\int_{t_0}^{t_1} v(t)^2 dt}
[/tex]
 

Related to Calculating RMS Value of i=1/3sin3t

What is the formula for calculating RMS value of i=1/3sin3t?

The formula for calculating RMS (Root Mean Square) value of i=1/3sin3t is:

RMS = (1/√2) x (1/3sin3t)

What is the significance of calculating RMS value for i=1/3sin3t?

Calculating the RMS value for i=1/3sin3t helps in understanding the average power of the given alternating current or voltage signal. It also helps in comparing different signals and determining their relative strengths.

How do I calculate the RMS value for i=1/3sin3t?

To calculate the RMS value for i=1/3sin3t, follow these steps:

  1. Square the function i=1/3sin3t: (1/3sin3t)^2
  2. Integrate the squared function over one period (2π/3): ∫ (1/3sin3t)^2 dt = 1/18
  3. Divide the result by the period: 1/18 / (2π/3) = 3/12π = 0.0796
  4. Take the square root of the result: √0.0796 = 0.282
  5. Multiply by 1/√2: 0.282 x 1/√2 = 0.2

Therefore, the RMS value for i=1/3sin3t is approximately 0.2.

What are the units of the RMS value for i=1/3sin3t?

The units of the RMS value for i=1/3sin3t depend on the units of the original function. In this case, since the function i=1/3sin3t represents a current, the units of the RMS value would be in amperes (A).

How does the RMS value for i=1/3sin3t compare to the peak value?

The RMS value for i=1/3sin3t is equal to the peak value (amplitude) of the function multiplied by 1/√2. In this case, the peak value would be 1/3 and the RMS value would be approximately 0.2.

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