# Integration for Power in an RL ac circuit

Discussion in 'Homework Help' started by Tera-Scale, Jan 14, 2011.

1. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
164
5
Does anybody have some good links on where I can read about deriving Power in an ac cycle for an LR circuit by integration. I have equations for instantaneous current and instantaneous voltage and even the impedance.

v=315sin(100pi*t)Volts
i=3.665sin(100pi*t-0.374)Amps
z= (80 + j10*pi)Ω

I manage to obtain the perfect graps for current voltage and power but the thing is that when I am integrating (definite) I am getting zero all the time :s

2. ### edgetrigger Member

Dec 19, 2010
133
19
integrate product of Vrms and Irms from 0 to 2∏, you'll get a finite non zero value.

3. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
164
5
I got a strange number :s ... what does it represent exactly? It's nowhere near P=(Vrms squared)/Z or P=(Irms squared) * Z

Since I have to comment between the different results obtained. The difference is huge from the result you told me (3626.89) and the P's i mentioned of 577.25Watts.

thanks

Brandon

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
As a check the average power would be Vrms*Irms*cos(θ)

Vrms=315/√2=222.74
Irms=3.665/√2=2.59

Hence

Pav=222.74*2.59*0.931=537W

5. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
164
5
Yes, I considered that check but now I am stuck on what and how to integrate. I am asked to find the power in the first cycle and what I did was finding the area of voltage of the first half(0-0.01) and then the 2nd(0.01-0.02) And the same for the current but everything cancels out. :s Why is it that i have a negative area of power on the second half when i plot the graph it wasn't that way.

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
Check this ...

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7. ### Tera-Scale Thread Starter Active Member

Jan 1, 2011
164
5
Lovely.. thanks buddy. One day I want to help other people like you. This summer I plan to contribute to this site in some way or another.

thanks again

Brandon