Question

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

Answer 1

We know that RMS is root mean square, we'll integrate it over a period
Period T=\(\large \frac{2\pi}{200\pi}=\frac{1}{100}\)
\[\large V_{rms}=\sqrt{\int_0 ^{1/100} \frac{1}{\frac 1{100}} (100\times \sin (200\pi+\pi/4) )^2dt}\]

Answer 2

?

Answer 3

@timtim do you get this?

Answer 4

with mobile number? ;P

Answer 5

@timtim now you need it to integrate it, can you do it?

Answer 6

no he cannt...

Answer 7

not sure how to integrate it
why is the period 1/100

Answer 8

sin t has period of 2pi seconds
sin 2t has period of 2pi/2=pi seconds
so
sin 200\(\pi\)t has period of \(\large \frac{2\pi}{200\pi}=\frac 1{100}\)

Answer 9

ok - understand that bit now so then it needs integrating

Answer 10

yeah, just integration:)

Answer 11

brb

Answer 12

10000/100(sin(200pi + pi/4)^2 dt
is that right

Answer 13

yeah

Answer 14

since it is sin^2 do i have to change to cos
i.e. 100 x 1/2 [1-cos2(200pi + pi/4)]

Answer 15

yeah:)

Answer 16

i now have squar route 50[1-cos400pi + pi/2]
how do i now integrate

Answer 17

\[\int \frac{1-\cos (400\pi t+\pi/2)}{2} dt\]

\[\frac t2 -\frac{\sin(400\pi t+\pi/2)}{2\times 400 \pi}\]

Answer 18

apply the limits now

Answer 19

@timtim do you get this?

Answer 20

substitute t for 1/100 and 0