# Which wave will generate more heat?

1. Sep 1, 2013

### 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.

2. Sep 1, 2013

3. Sep 1, 2013

### 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.

4. Sep 1, 2013

### milesyoung

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.

5. Sep 1, 2013

### Redbelly98

Staff Emeritus
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.

6. Sep 2, 2013

### samieee

Yes, amplitudes of all the waves are same.

7. Sep 2, 2013

### Redbelly98

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

8. Sep 3, 2013

Also assuming the loads are the same.

9. Sep 3, 2013

### KHMOU YOUSSEF

All the signals have the same frequency?

10. Sep 3, 2013

### Redbelly98

Staff Emeritus
Yes.

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.

11. Sep 4, 2013

### 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.

12. Sep 4, 2013

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

13. Sep 4, 2013

### Staff: Mentor

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

14. Sep 4, 2013

### Staff: Mentor

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

15. Sep 4, 2013

### mikeph

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