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Resistance and solar panels
<Photovoltaic water heater
100 watt solar panel
Back view                      Front view
Example Renogy mono-crystalline panel
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Buy from my affiliate links:
One 100 watt solar panel at Amazon $149
One 250 watt panel at Amazon $350
Two 150 watt panels at Amazon $300
Buy solar panels at Amazon
Branch wires
Mounting brackets


Specifications of the 250 Watt RENOGY panels
Maximum Power: 250W
Optimum Operating Voltage (Vmp): 30.1V
Optimum Operating Current (Imp): 8.32A
Panel Ideal resistance at 1000W/m^2 solar isolation = Vmp / 1mp 30.1V / 8.32A = 3.617 Ohms (per panel)



Resistance

Basis:
Watts stay the same with either parallel or series..
Volts x Amps = watts
Resistance (ohms) = volts divided by amps, V/I
Resource: Formulas-for-Ohms-law.html

Math:
Example: 120 volts x 15 amps = 1800 watt => 120/15 = 8 ohms
Example: 60 volts x 30 amps = 1800 watt => 60/30 = 2 ohms
.... this shows that resistance goes down when when amps go up...

Theory:
During high solar conditions, low resistance (higher amps) harvests more electric output.
During low solar conditions, higher resistance (lower amps) harvests more electric output.
ResourceHow to optimize-solar-panel-array.html

Application:
A string of 12 panels in series is best for low solar because it raises resistance (low amps) ... so amps are lower in a string and volts are higher. Note: transmission distances areincreased with high volts because less amperage means less heat loss on the wire.
While12 panels in parallel are best for high solar because resistance is low (high amps)  ...so amps are higher in parallel and volts are lower.

Choose high wattage or low wattage applications:
Resource:
Connect water heater to solar panels low voltage
Connect water heater to solar panels high voltage

Choose element rated for your output:
Volts and watts are printed on end of each element.
Ordinary elements work fine for AC or DC.
You can connect 100-250 volt 30 amp solar installation directly to residential water heater... except alterations are needed, otherwise the thermostat will melt. Read about converting to high voltage DC

In 2017, most local hardware stores do not carry elements rated for low volt and watt ratings, so you need DC element for those applications.


Single U and double U DC elements, 24 volt 500-900 watts.

The single U is ordinary residential water heater style with 2 screws to connect the wires. So your solar panels are connected directly to the element.
The double U element  has 4 screws for 4 wires and can accommodate two separate connections.... meaning you can have two separate sets of solar panels, and each set of solar panels can supply power to one of the U
3U elements are usually larger thread and will not fit a residential tank.

Buy:
DC elements
Single U 24 volt 600 watt element
Double U element
single U element
double U element
Resources
Solar PV safety
How to set up array
How to replace water heater elements
Figure volts amps watts
All solar links

Convert AC water heater to DC water heater/ high voltage

+++++++++++++++++
Typically in residential water heating, small water heaters (20 gallon) use 1000-1500 watt elements. Ordinary shower uses 10 gallons hot, ordinary bath uses 20 gallons hot.
You can set thermostat to higher temperature to get more miles out of a tank of hot.
http://waterheatertimer.org/Increase-amount-of-hot-water.html

Larger water heaters use elements with more wattage in order to heat the water.... if the tank is full of unheated water, it will cool the water that is heated.
A 500 watt element would struggle to heat a 40 gallon tank

5.866689  Kwh to raise 40 gallons of water 60F (starting at 60- and ending at120F)
Typical shower might be 104F
1000 watts for 1 hour is 1 Kwh
Your 500 watt element produces 1 Kwh for each 2 hours operation
So you would need 5.867 x 2 hours or 11.73 hours to heat a tank ... and that is with ideal conditions, no consumption of hot during those hours, full sunshine, no cooling of tank etc etc ... except the tank would cool, and sun is not dependable each day.
.. or if you satisfied with less-than-thermostat-setting hot water, say 80?
http://waterheatertimer.org/Kwh-temp.html

If you have a double U element, the time would be less.

Conclusion: the direct solar PV using low voltage DC elements plan would work best with a smaller (20-30 gallon), well insulated tank.... and that was the project I was planning at my house, except hadn't gotten around to it yet.


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