Rms current, complex area, phasors

[Bassalisk]

A lot of questions:

http://img846.imageshack.us/img846/4963/capture3jpg.jpg

http://img861.imageshack.us/i/captureh.jpg/

Find i2
Solution:
http://img847.imageshack.us/img847/3773/capture2g.jpg

Sorry for image spamming, i thought i should give you exact numbers and all so u can better understand what i am after.

My question here is, why is RMS voltage used in euler complex system, and not max voltage.

Is there any special reason or?

 

[waht]

why is RMS voltage used in euler complex system, and not max voltage

You can represent any sinusoid in terms of phasors regardless if it's RMS or not.

 

[LotusEffect]

We usually use rms voltage because this is what's important in power consumptions considerations and such.

For example, we say that the voltage of a common power outlet is 120 V which is its rms value. This allows easy calculations of power consumption because an ac voltage of 120 V rms will have the same effect on a 1 ohm resistor than 120 V dc.

 

[Bassalisk]

We usually use rms voltage because this is what's important in power consumptions considerations and such.

For example, we say that the voltage of a common power outlet is 120 V which is its rms value. This allows easy calculations of power consumption because an ac voltage of 120 V rms will have the same effect on a 1 ohm resistor than 120 V dc.

U didn't get what I asked. I am asking, why didn't we extract MAX voltage from original formulas(sinusoid) but we divided it by square root of 2, and then threw it into euler's formula?

 

[LotusEffect]

You could have kept the max voltage throughout. It's just that they convert it to rms value from the beginning because that's what is used in real life applications. Keeping the max value (amplitude) instead of rms value would do no harm to the equations. It's just that at the end you'd have ended up with the max values which are less relevant.

 

[Bassalisk]

Thats it? Pff i was hoping for "aha" moment. Thanks!

 

[Bassalisk]

But this RMS, why do we have that anyway? I mean if I apply 100 volts of AC, why do i get only 0,707 of that, and why that specific ratio?

 

[waht]

But this RMS, why do we have that anyway? I mean if I apply 100 volts of AC, why do i get only 0,707 of that, and why that specific ratio?

The RMS value is defined as:

What that means is that you are averaging voltage squared of a periodic function over a time interval, and then taking a square root to get the average. If you calculate RMS for a sine wave, you will end up with 0.707 factor. But for a triangle wave or a square wave or another complicated wave, RMS will be different.

 

[LotusEffect]

"Power-wise" you get less than Vmax because the voltage oscillates between -Vmax and Vmax!

Now for the 0.707, there is the proof here : http://en.wikipedia.org/wiki/Root_mean_square#Average_electrical_power.

 

[Bassalisk]

Yea i see that now, thanks <3

 

[UR_Correct]

I always teach kids to use RMS when you're dealing with power because then its P=VI* instead of P=1/2 VI*