<problem><script type="loncapa/python">
R = float(random.randrange(100,200,10))

Vrms = 120
Vp = math.sqrt(2)*Vrms
Pp = (Vp**2)/R
Prms = (Vrms**2)/R
</script><startouttext/>
The plot shows 1/10 second of the voltage waveform of a 120V 60Hz AC
(Alternating Current)
power circuit, like that delivered to residences in the United States.
<center><img src="/static/circuits/120V60Hz.gif"/></center>
The actual voltage is \(120*sqrt(2)*cos(2*\pi*60*t)\)Volts.  If we apply
this voltage across a resistor of resistance \($R\Omega\) the resistor
will dissipate a time-varying power.
What is the peak power (in Watts) dissipated by the resistor?
<endouttext/>
<numericalresponse answer="$Pp"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>

<startouttext/>
<br/> What is the average power (in Watts) dissipated by the resistor?  (Hint: you
  compute the average power by integrating the power over one cycle of
  the waveform.)
<endouttext/>
<numericalresponse answer="$Prms"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>

<startouttext/>
<br/> What would be the power (in Watts) dissipated by the resistor if the voltage
  was a constant value of 120V?
<endouttext/>
<numericalresponse answer="$Prms"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>

<startouttext/>
<br/> If a time-varying voltage dissipates the same power in a resistor
as a constant voltage would dissipate, we say that the time-varying voltage has
the RMS value of the constant.  RMS is an abbreviation for Root-Mean-Square.
<endouttext/>


</problem>
