Question

what is the rms value of the voltage
u(t) = 3 + 4 cos (3t)

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Answer 1

Answer:

Let's say it's just it's a variable. So the function will be

u(t) = 3 + 4 cos (3t)

RMS value of a function is given as follows

Yrms= Lim T->INF (Sqrt (1/T (Integral from 0 to T ( Y^2 dx))))

For periodic functions, calculating to infinity is same as calculating for 1 period.

The period of 3+4cos(3t) is 0 to 120 degree or 0 to 2pi/3 radians

The value of the integral is.

Integral between 0 and 2pi/3 (( 3+4coc(3t))^2) dx

The expansion of the term to be squared is

9+24cos(3t)+16cos(3t)^2

Whose integral is

9x+ 24sin(3t)+8x+4sin(6t)

Substituting the limits

6pi+0+16pi/3+0

34pi/3

Dividing this by the period width 2pi/3

We get 17

So RMS value is square root of 17 which is 4.123

Answer 2

Answer:√17

Explanation: