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Physics/Peak current and rms and frequency


Current through a 50ohm resistor is I=0.8sin(240t). What is the rms current? At what frequency does it vary? What is the power dissipated in the resistor?

I don't know how to approach this question since it's an equation. I do know the 0.8 refers to the current, but I'm not sure how to find the others.

Hello Sona,

The peaks of the current, if you watched on an oscilloscope, would be +0.8 A and -0.8 A. When the waveform is a pure sinewave (and that would be true here), RMS is the peak value multiplied by the square root of 1/2. Therefore
Irms = 0.8*0.707 Arms (or just A if it is understood that we are talking about an rms measurement.)

The 240t part gives the information to calculate frequency. As time advances, the argument for the sine function increases. So if you plot points, I versus t, you get a sine wave. When t advances from zero until 240t is equal to 2*pi, it has gone through one cycle of the oscillation. So
if 240*t = 2*pi, then t = 2*pi/240 = 0.026 sec
That is the period, T, of the oscillation, so the frequency is given by
f = 1/T

One advantage of an RMS measurement, is for power calculations. If this were a DC current, power is just P=I*R^2. If it is an AC current it can be more complicated because the amplitude keeps changing. But if you have an RMS measurement for I, then you can use

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
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