Power across resistor with a 50Hz source

[mull982]

I know that the power through a given resistor is calculated by V^2/R where V is the RMS value of the voltage. So for example with 120V dropped across a 10ohm resistor the power dissipated across the resistor would be 1440watts. This of course is assuming a 60Hz source.

What if however we were performing this same calculation with a 50Hz source? Would we have to calcultate a different RMS voltage?

Since RMS voltage is 1/T *(integral of x^2) and since the period or "T" value in this equation would be smaller for a 50Hz signal would the Vrms voltage for a 50Hz signal be higher than that for a 60Hz signal? If that is the case, then would there be more power dissipated across the 10ohm resistor for a 50Hz signal than with a 60Hz signal?

 

[broadgage]

The power disipated in a resistor is independant of frequency.

A 240 ohm resistor connected to a 120 volt supply will draw 0.5 amps and disipate 60 watts, no matter what the frequency may be, or on DC.

AC voltages, unless stated otherwise, may be assumed to be RMS voltages, no additional calculations are required.

1 amp DC or AC RMS through a given resistance will allways produce the same heating effect.

 

[rattus]

The reason is:

The reason is:

Mull,

The period "T" would be longer (20ms) for 50 Hz, but the limits of integration would also be longer (0-20ms) which means that 6/5 times the energy would be dissipated in a 50hz cycle. "T" would also be 6/5 times as long, therefore the ratio remains constant--independent of frequency.

 

[Speedskater]

As a side note: At very high frequencies, many real world resistors are no longer perfect resistors and become a resistor with a series inductor.

 

[mull982]

Mull,

The period "T" would be longer (20ms) for 50 Hz, but the limits of integration would also be longer (0-20ms) which means that 6/5 times the energy would be dissipated in a 50hz cycle. "T" would also be 6/5 times as long, therefore the ratio remains constant--independent of frequency.

That makes sense

So for a 50Hz AC signal with a peak voltage of 170V would that RMS voltage still be 120V as it would be with a 60Hz signal?

 

[rattus]

Yes:

Yes:

That makes sense

So for a 50Hz AC signal with a peak voltage of 170V would that RMS voltage still be 120V as it would be with a 60Hz signal?

Absolutely! In the derivation of the effective value factor, 0.707, "T" and "w" fall out. "T" can be any value other than zero or infinity.