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Which wave will generate more heat?by samieee
Tags: square wave 
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#1
Sep113, 11:07 AM

P: 71

Suppose there are some waveforms to be used as current input: i)sine wave ii)square wave iii) triangle wave iv)sawtooth wave and v)sawtooth wave with both the cycles(+ve half cycle and ve half cycle) in positive Y axis. Which wave will generate more heat?
Actually, I faced this question in a recent examination. Though I ansewered (v), now I think the right answer would be square wave, as it grabs the maximum magnitude for more duration of time than the others. Am I right? Thanks. 


#2
Sep113, 11:56 AM

P: 527

Assuming it's the waveform of the current through a resistor, you should have a look at how the RMS value of the waveform relates to the power dissipated in the resistor:
http://en.wikipedia.org/wiki/Root_me...ectrical_power Then you can compare the RMS values of your different waveforms: http://en.wikipedia.org/wiki/Root_me...mmon_waveforms 


#3
Sep113, 01:03 PM

P: 71

So, from the comparison, I see that square wave has the higher value than any other rotating wave. DC shifted square wave has even higher value as it should have.



#4
Sep113, 02:29 PM

P: 527

Which wave will generate more heat?
The instantaneous power delivered to the resistor is ##p(t) = R i(t)^2##. If you try to imagine the graph of ##p(t)## for your waveforms, it should confirm your idea of why its average value is highest in the case of the square wave. 


#5
Sep113, 04:19 PM

Mentor
P: 12,071




#6
Sep213, 04:07 AM

P: 71




#7
Sep213, 09:21 AM

Mentor
P: 12,071

Okay. So yes, it is the square wave. As milesyoung said, you need to consider [itex]i^2 R[/itex].



#8
Sep313, 09:31 AM

P: 564

Also assuming the loads are the same.



#9
Sep313, 10:39 AM

P: 6

All the signals have the same frequency?



#10
Sep313, 05:52 PM

Mentor
P: 12,071




#11
Sep413, 12:55 AM

P: 106

The real question is could you make a saw tooth laser beam if you super imposed different frequencies on top of each other. Not sure how this could be accomplished but its an interesting thought.



#12
Sep413, 07:42 AM

P: 564

Huh? Lasers operate at one frequency, i.e perfect sine wave oscillation, unless you mean to modulate the laser?



#13
Sep413, 11:34 AM

HW Helper
Thanks
P: 5,364




#14
Sep413, 11:40 AM

HW Helper
Thanks
P: 5,364




#15
Sep413, 02:42 PM

P: 1,212

or you could modulate the injection current to get a sawtooth amplitude at some frequency << lasing frequency



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