<problem><script type="loncapa/python">
V = 240
P = float(random.randrange(800,1600,10))
Pmax = 3*P
Imax = Pmax/V

Iq = Pmax/120

R = (V**2)/P

Rbad = 3*R/2

Pbad = (V**2)/Rbad

Ibad = Pbad/V

PH1 = (Ibad**2)*R
PH2 = ((Ibad/2)**2)*R
PH3 = PH2
</script><startouttext/>
Joe wants to heat his 12'X20' workshop with electric heat.  He has
hired the HACME electrician company to build the system.  They propose
to use three \($P\)W 240V baseboard heaters to provide a total heating
capacity of \($Pmax\)W.  (A heater is basically a
resistor.  This is not quite true, because there is a thermostatic
switch incorporated into the heater and because the resistance of a
heater varies a bit with its temperature.  But we will use a linear
resistor as a model of a heater.)
<br/>
In the proposed system the heaters are connected in parallel with the
240V 60Hz AC power line (modeled by a voltage source) as shown in the
diagram:
<center><img src="/static/circuits/heaters-parallel.gif"/></center>
Remember (from exercise S1E3: AC POWER) that AC power-line voltages
and currents are specified as RMS values.  So 120V AC heats a given
resistance exactly as much as 120V DC would heat that same 
resistance.
<endouttext/>

<startouttext/>
<br/>
How much current is expected to be drawn from the power line by this
heating system when all three heaters are on?
<endouttext/>
<numericalresponse answer="$Imax"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
<startouttext/>
<br/>
If instead, HACME chose to implement the system with 120V heaters, how
much current would have been needed?
<endouttext/>
<numericalresponse answer="$Iq"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
<startouttext/>
<br/>
Notice that this would require much heavier and more expensive wire to
distribute the power.  
<br/> <br/>
Back to the original plan with 240V power.
<br/>
Unfortunately, Sparky, who works for HACME, was a little sleepy that
day.  He accidentally connected the heaters as shown below:
<center><img src="/static/circuits/heaters-bad.gif"/></center>
<br/>
As a consequence, Joe found his workshop too cold.  H1 was weak; H2
and H3 barely warmed up.
<br/>
What power was being dissipated in H1?
<endouttext/>
<numericalresponse answer="$PH1"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
<startouttext/>
<br/>
What power was being dissipated in H2 (or in H3)?
<endouttext/>
<numericalresponse answer="$PH2"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
<startouttext/>
<br/>
So the total heating power in Joe's shop was:
<endouttext/>
<numericalresponse answer="$Pbad"><responseparam type="tolerance" default="5%" name="tol" description="Numerical Tolerance"/><textline/></numericalresponse>
<startouttext/>
<br/>
<!-- add non-ascii utf-8 character here -->
No wonder Joe was cold…
<endouttext/>

</problem>
