Which wave will generate more heat?

[samieee]

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.

 

[milesyoung]

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_mean_square#Average_electrical_power

Then you can compare the RMS values of your different waveforms:
http://en.wikipedia.org/wiki/Root_mean_square#RMS_of_common_waveforms

 

[samieee]

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.

 

[milesyoung]

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.

Right, so your intuition with regards to the square wave was spot on.

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.

 

[Redbelly98]

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?

This question cannot really be answered as stated here. Are the amplitudes of all the waves supposed to be the same? That needs to be specified.

 

[samieee]

Are the amplitudes of all the waves supposed to be the same? That needs to be specified.

Yes, amplitudes of all the waves are same.

 

[Redbelly98]

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

 

[Windadct]

Also assuming the loads are the same.

 

[KHMOU YOUSSEF]

All the signals have the same frequency?

 

[Redbelly98]

Also assuming the loads are the same.

Yes.

All the signals have the same frequency?

That does not matter. The average of i² is the same no matter what the frequency is. Just for example, for a sine wave, it is (1/2) the square of the amplitude, independent of the frequency.

 

[rppearso]

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.

 

[Windadct]

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

 

[NascentOxygen]

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?

That's the beauty of the RMS value, it directly relates to the heating value (in a resistive load).

 

[NascentOxygen]

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

Wouldn't frequency-doubling lasers allow you to generate some coherent harmonics?

 

[mikeph]

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