Electronics and Communication Engineering - Networks Analysis and Synthesis - Discussion

RMS or root mean square is the SQUARE ROOT of an area of a specific function SQUARED times (1/2) because of the word MEAN or AVERAGE value. In the given curve, it is divided into two parts.

1. From t = 0 to t = 1, the function is V = 100t (as you can see the value of V is 0 at t = 0 and 100 at t = 1 OR just use point slope form).

2. From t = 1 to t = 2, the area is like a square with sides measuring 100 units.

Therefore:
vrms = √{(1/2)(A1 + A2)},
Where:
A1 = Integral (100t)^2 dt, t = 0 to t = 1.
A2 = Integral (100)^2 dt, t = 1 to t = 2.

RMS value means root mean square which by its name only suggests that it is nothing but the square root of mean of squared value of voltage or any quantity to be measured. In this case the function is voltage which can not be represented by a single function.

So the interval of investigation should be broken into respective number sub-intervals where the voltage function can be represented by a single algebraic functions. After getting the square of the functions and do the same as explained in first line.

The given signal consists of a ramp signal plus a dc signal.

The ramp signal has the RMS value of Vp/√(3).
the dc signal has the RMS value of dc value itself.
the total RMS value is;
√{(100^2)/3 + 100^2}.

This results 200/√(3).

RMS= Root of Mean of Square.

As per the given formula...from 1to 2 it is 100^2.
=> root{1/2[10^4 + 10^4x[1/3] ]}.
=>root{1/2[10^4x[4/3] ]}.
=>root{10^4 x 2/3}.
=>100 x root{2/3}.
=>81.someting.
= 80(approx).

Because from 0 to 1 it is slope function, y=mt use this formula you will y = 100t.

m = 100 i.e, slope. m = (y2-y1)/(x2-x1).

RMS = (1/2) (Integral (x (t)^2))^(1/2).

Actually, in the first integration the ramp signal is taken so it is 100t and in second integration the step signal is taken 100 (magnitude).

From 1 to 2 it should be 100^2.

And if we use 100^2 then answer is different.
And if we use 100 only still the answer is different.

I did not under stand you are explanation can you give me more explanation about rms value.

Why (100t) ^2 in a triangle and only 100t in rectangular? Explain, please.

Why the slope m=100 it is 100v.

How it is, please explain.