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Author Topic: AC Power calculation from current  (Read 19917 times)
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Fu-Kwun Hwang
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on: September 13, 2010, 10:30:06 pm » posted from:,,Taiwan

The power loss due to current I(t)=A\, \sin\omega t for resistor R is
P=I^2R=A^2\, \sin^2\omega t \, R=A^2 \frac{1-\cos 2\omega t}{2} \, R

The following applet draw 3 curves
1. A\, \sin\omega t

2. A^2\, \sin^2\omega t

3. B -\frac{A^2\cos 2\omega t}{2} where B can be adjust by right slider from 0 to \frac{A^2}{2}


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* sin2.gif (57.61 KB, 676x478 - viewed 618 times.)
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lookang
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Reply #1 on: September 14, 2010, 04:23:26 pm » posted from:SINGAPORE,SINGAPORE,SINGAPORE

i always wanted to make this!

My input to the applet.
corrected some typo for the applet.
added some design to the layout
added omega w


comment!
good work prof hwang Smiley
this applet will be a good tool for student learning, they usually cannot understand the transformation of the curve from
 "A*sin(w*t)" to ("A*sin(w*t)")^2 as this applet aims to visually represent.

question,
how do you use the blue "B-A*A*cos(2*w*t)/2" to allow learning of average power in AC circuit calculation?

my teaching approach
i normally use only the red curve
"A*sin(w*t)"
and the black curve
"A*A*sin(w*t)*sin(w*t)"
only.


other student learning difficulty and suggestion for applet ?
the other part is the area under the curve "A*sin(w*t)" to ("A*sin(w*t)")^2 is half of the rectangle form by A*A and the period T. student cannot visualize this i feel.
i guess i could use Ejs data tool to find area under the curve to show that.

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Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
  • Please feel free to post your ideas about how to use the simulation for better teaching and learning.
  • Post questions to be asked to help students to think, to explore.
  • Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!


* acpower.PNG (65.92 KB, 715x560 - viewed 630 times.)
« Last Edit: September 14, 2010, 04:35:29 pm by lookang » Logged
lookang
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Reply #2 on: September 14, 2010, 06:33:33 pm »

The power loss due to current I(t)=A\, \sin\omega t for resistor R is
P=I^2R=A^2\, \sin^2\omega t \, R=A^2 \frac{1-\cos 2\omega t}{2} \, R

oic, the blue line is to show Power loss in R =A^2 \frac{1-\cos 2\omega t}{2} \, R
i see now Smiley
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Fu-Kwun Hwang
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Reply #3 on: September 14, 2010, 11:42:11 pm » posted from:,,Taiwan

Quote
other student learning difficulty and suggestion for applet ?
the other part is the area under the curve "A*sin(w*t)" to ("A*sin(w*t)")^2 is half of the rectangle form by A*A and the period T. student cannot visualize this i feel.

That is exactly why the above applet was designed for.

Black curve I^2(t) is the square of the red curve I(t).
However, it is similar to Blue curve (when B=0), the only difference is there is an offset.
And the offset (difference between black curve and blue curve is a constant)
 which is always half the maximum value of black curve(independent of A or \omega).

i.e. The offset is \frac{A^2}{2}.
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ahmedelshfie
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Reply #4 on: September 15, 2010, 05:35:49 pm » posted from:SAO PAULO,SAO PAULO,BRAZIL

Find it using search by google.
URL  http://powerelectrical.blogspot.com/2007/02/ac-power.html
The above graph shows the instantaneous and average power calculated from AC voltage and current with a lagging power factor (φ=45, cosφ=0.71).
Average power is the real power and instantaneous power is the apparent power.



* ac power2.png (33.43 KB, 300x247 - viewed 1041 times.)
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Fu-Kwun Hwang
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Reply #5 on: September 15, 2010, 05:50:44 pm » posted from:,,Taiwan

The applet for this topic is related to the power loss of an resistor P(t)=I(t)V(t)=I^2(t) R The voltage and current are in phase.

The URL you referer to is another issue:
 AC Power due to phase different between current and voltage (RC or RL circuit).
It is a different story!
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Fu-Kwun Hwang
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Reply #6 on: September 17, 2010, 04:09:36 pm » posted from:,,Taiwan

Quote
other student learning difficulty and suggestion for applet ?
the other part is the area under the curve "A*sin(w*t)" to ("A*sin(w*t)")^2 is half of the rectangle form by A*A and the period T. student cannot visualize this i feel.

A^2\sin^2\omega t + A^2\cos^2\omega t=A^2
Let's calculate the average on both side.
The average of A^2\sin^2\omega t should be the same as average of A^2\cos^2\omega t
And the sum of the above two average is A^2
So the average of A^2\sin^2\omega t equal to \frac{A^2}{2}
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