# Does a resistor in an AC circuit produce the same heat as in a DC circuit?

Does a 1k ohm resistor produce the same heat in a AC circuit which has an rms voltage of 10 volts (60 hz.) as it would in a 10 volt DC circuit?

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Is this a homework question? – Gustavo Litovsky Feb 21 '13 at 1:19
No... Why? Did I do something wrong? I stopped doing homework a few years ago. – Vicky Feb 21 '13 at 1:29
Editing the question has changed the scope of answer @Vicky. Now it leans more towards yes :P – D34dman Feb 21 '13 at 1:51
@Vicky: No. Just checking. It looked like homework and that's frowned upon here without any research. – Gustavo Litovsky Feb 21 '13 at 1:52
@D34dman i'm not experienced here... should I change it back? – Vicky Feb 21 '13 at 18:21

Edit

This answers the original version of the question, which asked,

Does a 1k ohm resistor produce the same heat in a AC circuit which has an average voltage of 10 volts (60 hz.) as it would in a 10 volt DC circuit?

No, the heat produced depends on V2, not V.

As a simple example, consider a sinusoidal AC signal with 10 V peak to peak, and 0 DC component. The average voltage is zero, but it still delivers power to the resistor and the resistor still heats up.

To get the heat produced in the AC circuit to be the same as in the DC circuit, you want the rms voltage (The square root of the mean of the square of the voltage) in the AC circuit to be equal to the DC voltage in the DC circuit.

Edit: As D34dman points out in his answer, there are some special cases where the rms voltage and average voltage happen to work out to the same value.

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Thanks ThePhoton! +1 – Vicky Feb 21 '13 at 18:23

Provided frequency is high enough, 1k ohm resistor in an AC circuit would produce same heat (a.k.a. power converted as heat ) as as it would in DC circuit provided the RMS (Root Mean Square) value of supplied Voltage is same.

You can read this wiki entry to know more. Proceed to section Average electrical power.

RMS value is dependent on the the nature of AC waveform. RMS value is not always equal to average value. But they can be equal. For example a square wave alternating between 0 and Vpeak with 50% duty cycle they can be equal.

So to answer your question, if you are giving an AC waveform such that its RMS value and Average value is the same, it would produce same heat. If they are different it wont.

I felt compelled to write this answer since @The Photon has some misguided information in his answer. Maybe he assumed that AC signals are necessarily pure sine wave type which goes from +Vpeak to -Vpeak. Which is just a subset of AC signals.

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that was "a simple example". A pure sine wave is an example of an ac signal. It is not the only kind of ac signal. I re-worded a bit to be more specific. – The Photon Feb 21 '13 at 1:52
And then the asker has changed his question and removed average altogether :/ Making our explanation about average not required anymore. – D34dman Feb 21 '13 at 1:58

If it's a "perfect" resistor, yes.

But if it has parasitic inductance or capacitance (as all real examples will, except at their self-resonant frequency where the two cancel) then, no, not exactly, though with the exception of wirewound resistors the difference will be small.

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