Need help with design issues - resistor questions

Hi all, thank you for your help up front - i have been beating my head on my workbench for a couple weeks now. I am new to the electronics world, but I have tried to do as much research as I could.

I have a couple questions;
1: I have a 48 V power supply (12.5 A). Its feeding a number of thermoelectric Peltier plates (see image of schematic), each plate draws 14.4 Vmax and 6.4 Imax. I need the top layer of plates to be colder then the bottom layer, thus why i have two pairs wired in series, then a group of 4 wired in series. By my math using Ohm's law, the resistors I need for the first two pairs is : (14.4 * 2) = 28.8. 48V -28.8V = 19.2V 19.2V / 6.4a = 3Ω ....? right ???

so my understanding is that the first two pairs need a 3Ω resistor. Now, with 48v power supply feeding 12.5amps I connected a 25Ω potentiometer to test this after adjusting it down to around 4 ohms resistance...and I fried my pot. So that made me question if at 1/4 or 1/2 watt resistor will do the job. I tried looking this up in the forums here but could not find a definite answer. Will a 1/2 watt resistor do the job for the current i am putting through it?

Question 2: should I be wiring the first two pairs of plates in parallel instead of in series? I have enough current to supply two disks in parallel, but am not sure if this is an advantage for me or not.

Thanks again for any feedback / suggestions

 

Great info! thank you so much - I will post an update when i have it working.

 

Thanks Colin, that is an issue for this project as I need to try and Max out the current for the top array of peltier plates so they get as cold as possible.

Hevans1944 - I have done some research on the Pulse Width Modulation using a MOSFET transistor. This is a handy bit of skills that I can use on other projects - thank you again. I have some questions however. My understanding (summarized ) is that the PWM takes the avg from 0 to some maximum voltage - in my case 0 to 48 V to create a duty cycle (based on the frequency of this cycle) that gives my device a voltage of whatever I need. So if I need 14 volts, i would calculate the duty cycle to give me roughly 30% of the max voltage thus supplying the 14 that I need.

My concern is that if my peltier plate has a Vmax of 14.4 volts, is this cycling of 0-48V at a given frequency going to cause any damage to my device? I understand that it ends up getting an avg between the two - but I don't want to fry the peltier plate either.

My thoughts is to use an Arduino that has PWM management running through a MOSFET transistor to control each of the 4 top layer Peltier plates, then just connect the bottom array of plates in series (like in the schematic) because they dont need to be maxed out like the top array. Does this sound like I'm on the right path?

Thanks,