Determine the rms value for the given function

In summary, the rms (root mean square) value is a way to measure the magnitude of a varying quantity over time, such as voltage or current. It is calculated by taking the square root of the average of the squared values of the function over one period, or as the integral of the square of the function divided by the period. This value is important in electrical engineering as it allows for accurate comparisons and calculations in circuit design. It differs from the average value in that it takes into account the squared values of the function. Additionally, the rms value is always a positive value and cannot be negative.
  • #1
Northbysouth
249
2

Homework Statement



Determine the rms value of v(t) = 15 + 10cos(20πt)


Homework Equations



Vrms = √(1/T*∫T0v2dt

The Attempt at a Solution



√(10*∫0.10[15+10cos(20πt)]2dt

Unless, I'm much mistaken I should be able to plug the equation into the formula I have given above. I used the integral function on my calculator to do the calculation and I got 24.98V but the answer is supposed to be 16.58V

Any suggestions for where I'm going wrong?
 
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  • #2
Your setup is correct. You must have made a mistake in the integration with your calculator.
 
  • #3
Vrms = √15^2+(10/√2)^2 = 16.58 V
 

1. What is the definition of rms value?

The rms (root mean square) value is a way to measure the magnitude of a varying quantity over time, such as voltage or current. It is the square root of the average of the squared values of the function over one period.

2. How is the rms value calculated?

The rms value is calculated by taking the square root of the average of the squared values of the function over one period. This can also be written as the integral of the square of the function divided by the period.

3. Why is the rms value important in electrical engineering?

The rms value is important in electrical engineering because it is a way to measure the effective value of an alternating current or voltage. It allows us to compare the power of different signals and make accurate calculations for circuit design.

4. What is the difference between rms value and average value?

The average value of a function is simply the average of all the values over one period. The rms value takes into account the squared values of the function, which gives a better representation of the overall magnitude of the function.

5. Can the rms value be negative?

No, the rms value cannot be negative. It is always a positive value since it is the square root of the average of the squared values of the function.

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