UP-DOWN-UP-DOWN-UP-DOWN! Life has its own rhythm to go. In the run of life cycle it has ups and downs maybe that makes life to be more interestingly complete. It changes its direction anytime.
AC current also have a nature of changing its direction after a certain up its obvious for AC current/Voltage to face a down and then if we let it to continue it would repeat/replicate that same up-down cycle. The transformed (maybe by the induction of the coils as Faraday’s Law of Electromagnetic Induction states) power of the huge current produced in the power plants that the power generation company supplies us is theoretically a sine wave. (Practically its more naughty and dirty in nature and in country like us (by not putting U and S capital, i meant: our Bangladesh), PDB also sometime provides DC current, which has an ZERO AMPERE of constant currents, yes i am talking about the load shedding which neither alters its direction for hours).
AC current or voltage may not look like our so called sine wave (equation: x = Sin y), it may also look to be more like square or triangular waves. But as in square form or in the triangle form they are also alternating its direction They are AC currents as well. And another thing is, square or triangle waves can also be represented by summation of multiple sine functions.
Of a waveform the time it takes to make a single of that replicated part is the Period(T) of that wave. The time it takes for each of this cycle is called frequency(f). f=1/T
at T time it travels 2∏ circular path
so at 1s it travels 2∏/T path,
so circular velocity ω=2∏/T
when current starts to increase from 0V or 0A,
at any time of t, instant voltage will be:
v = Vmax sin ( ωt)= Vmax sin ( 2∏/T) = Vmax sin ( 2∏f)
instant voltage will be:
i = Imax sin (ωt) = Imax sin ( 2∏/T) = Imax sin ( 2∏f)
if voltage/current is greater than the equilibrium voltage or current, then the angle it need:
v = Vmax sin ( ωt + θ ), θ is the shift of angle from 0rigin .
RMS (Root Mean Square) Voltage is the avg Voltage of a AC source produce in its each cycle that we assume as direct source.
To measure RMS we have to follow 3 steps: 1. (S)quare 2.(M)ean 3.(R)oot.
At the interval of t1 and t2, Mean Square Voltage Vms ,
Vms = ∫Vmax sin² (ωt ) dt/(t2-t1)=Vmax/(t1-t2) ∫ ((1 – cos (2ωt )/2 )dt
=Vmax/2(t2-t1) ∫ (1 – cos (2ωt ))dt
=Vmax/2(t2-t1) ( (t2-t1) – sis (2ω (t2 – t1) )/2ω)
but since the interval is a whole number of complete cycles, the sin terms will cancel out, leaving:
Vms = Vmax (t2-t1) /2(t2-t1)
Rooting both side:
Vrms = Vmax/√2
This is enough that i have learned as an introduction of the very beginning of AC!
Now i want to scrap this blog post with a little word of humbleness, to a spacial friend who kept visiting on my blogs even at the time infect when there was nothing to visit at all (I also doubt! If it still has anything or not!) and elevated my visit counter to reach 200+. But the irony is after the bell of 200th visit rung he is like “never coming back once again” and my visitors list has given up to go increase :P.
And thankyou all who have ever contributed to this 200+ visits, This is ALOT to me!
The truth is, i am not the ONLY one who reads my blogs! 😉