# Thread: Root Mean Square Value

1. ## Root Mean Square Value

Question: show that the RMS value of current
$i = 4sin100 pi T$ is 2.828A
$NOTE: sin^2 theta = 1/2 (1-cos2theta)$

I have tryed to rearange the forumle inorder to work out T
$4sin 100= i X pi T$
T=4sin 100 i X pi
4sin 100 = 3.939 (2.828 X pi) = 34.99
T=34 but i dont think thats right.
can anyone help me.

2. Originally Posted by batman121
Question: show that the RMS value of current
$i = 4sin100 pi T$ is 2.828A
$NOTE: sin^2 theta = 1/2 (1-cos2theta)$

I have tryed to rearange the forumle inorder to work out T
$4sin 100= i X pi T$
T=4sin 100 i X pi
4sin 100 = 3.939 (2.828 X pi) = 34.99
T=34 but i dont think thats right.
can anyone help me.
The formula for a continuous function $f(t)$ defined over the interval $T_1 \le t \le T_2$ is

$
I_{\mathrm{rms}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {[i(t)]}^2\, dt}}
$
$
I_{\mathrm{rms}} = \sqrt {{1 \over {T}} {\int_{0}^{T} {[4\sin 100\pi t]}^2\, dt}}$

$I_{\mathrm{rms}} = \sqrt {{8 \over {T}} {\int_{0}^{T} (1 - \cos200\pi t)\, dt}} \\$

$I_{\mathrm{rms}} = \sqrt {{8 \over {T}} T} \\$

$I_{\mathrm{rms}} = \sqrt {8} A\\$