Question

V = 100 sin (200πt + π/4)
using integral calculus, calculate the RMS value of the voltage

Answer 1

Depends on your limits of integration... for example, at 60Hz:
\[\large\int\limits_0^{60} 100 \sin(200 \pi t+\frac{\pi}{4}) dt = 0\]

PS: This should be in Physics, IMHO.

Answer 2

But I'm going to assume you meant this...

Answer 3

\[\sqrt{\frac{1}{n} \left\{ x_1^2+x_2^2 + ... + x_n^2 \right\}}\]

Which turns into...

Answer 4

it is part of my maths course work

Answer 5

\[\large f_{RMS}(t) = \sqrt{\frac{1}{T_{final}-T_{initial}} \int\limits_{T_{initial}}^{T_{final}} (\ f(t)\ )^2\ dt}\]
\[\large f_{RMS}(t) = \lim_{T \rightarrow \infty } \sqrt{\frac{1}{T} \int\limits_{0}^{T} (\ f(t)\ )^2\ dt}\]


So... the INDEFINITE integral of your integral is? :-) (first step)

Answer 6

@timtim , Still with me? Bring out the 100 constant, let u = 200 \(\pi\) t+\(\frac{\pi}{4}\)

Answer 7

i am trying to follow but this is quite a jump from other questions i have been doing

Answer 8

It's been awhile since I've done this, I've just known the formula that you end up with when just trying to find the RMS voltages:

\(\large V=\frac{V_o}{\sqrt{2}}\) \(\leftarrow\)works only for sine waves

It's just V for DC constant or special case square waves (although \(\pm\) back and forth every cycle), and for sawtooth or triangle waves:

\(\large V=\frac{V_o}{\sqrt{3}}\) \(\leftarrow\)works only for triangle or sawtooth waves

Answer 9

To do the integral part, you'll need to follow the steps above and then integrate as you see in that last formula for the function\(_{RMS}\).

Answer 10

Integrate it and I'll check you

Answer 11

ok i will give it a try