*** The information contained in this post applies to all dual coil systems including cartomizers, clearomizers, and RBAs ***
INTRODUCTION
As the name implies, dual coil systems make use of two individual heating coils within a single delivery device. These two coils are wired in parallel (this is important) and are typically of equal resistance. The fact that they are of equal resistance just so happens to simplify the equations involved in understanding this topic quite a bit. In fact, when these two coils are the exact same resistance you can simply divide that resistance value by two in order to see what resistance your PV will read the dual coil setup as. This means that if you have two 4 ohm coils wired in parallel, your PV will read the resistance as 2 ohms. Why is this the case, you ask? Read on to find out!EXAMPLE #1
For the first example, assume there are two 4 Ohm coils (referred to as R1 and R2) wired in parallel. This will read as 2 Ohms when you check it on your PV or an ohmmeter. The 2 Ohm value is called RT, which represents total resistance. While the concept of dividing the resistance value by 2 may sound easy enough, this method only works out for you if both coils are the exact same resistance. Furthermore, two 4 Ohm coils wired in parallel is not the only way to arrive at 2 Ohms total resistance. The reason for this can be found in the formula used when solving for total resistance of a parallel circuit containing 2 resistances of any value. See the formula below.RT = 1 / (1/R1 + 1/R2)
What this formula means is that the total resistance RT (the resistance your PV will read) is equal to the reciprocal of the sum of the reciprocals of R1 and R2. That may be a mouthful, but see the example below where we can prove this to be true by plugging our resistance values into this formula:
RT = 1 / (1/4 + 1/4) = 2
As the above equation proves, two 4 Ohm resistors wired in parallel will yield 2 Ohms total resistance which is what your PV or ohmmeter will show. This is an especially "neat" way to look at the problem, because with two equal resistors wired in parallel they will receive the same voltage (V) and the same current (I). For the purpose of the following example, we will assume the PV is set to output 5 volts.
The total current (I) generated by your PV can be found by dividing V by RT. You can see this represented as a formula below with the answer:
IT = V / RT = 5/2 = 2.5 amps
So now we know that 2.5 amps is our total current, but what about the current going through each individual coil? It just so happens that since we are providing 5 volts, each coil will get 5 volts (note that this would be true regardless of their respective resistance values). In other words, VT = VR1 = VR2 = 5 volts. Since we know the voltage of each coil, we can find the current of each coil by dividing this number (5) by the resistance of each coil. You can see this represented as a formula below with the answer:
IR1 = VR1/R1 = 5/4 = 1.25 amps
Since R1 and R2 are exactly equal values, they will have the same current. So in this case, IR1 = IR2 = 1.25 Amps. Notice how we can add IR1 and IR2 to get IT (this is also important):
IT = IR1 + IR2 = 1.25 + 1.25 = 2.50 amps
The final thing we will solve for in this nice, neat example is power. One way to solve for power is to multiply voltage by current. If we want to determine the power dissipated by R1 (PR1), we can simply multiply V by IR1. See below for this written as a formula with our numbers plugged into it.
PR1 = V * IR1 = 5 * 1.25 = 6.25 watts
Furthermore, since R1 and R2 are equal, we can safely say that PR1 = PR2 = 6.25 watts. In other words, each coil is dissipating 6.25 watts. In order to find the total power (PT), simply add PR1 to PR2. See the formula and answer below.
PT = PR1 + PR2 = 6.25 + 6.25 = 12.50 watts
Continue below to see what happens when the resistances are not equal (it's about to get real)!
EXAMPLE #2
Now, let's take a look at another way to achieve an RT of 2 Ohms. This time instead of having nice, neat equal resistors we will use coils with resistances that are not equal (this will force us to gain a better understanding of the formulas- fun, right?). Note that this section of this post is mostly for theoretical purposes and to increase your understanding of what is really going on. According to the formula for total resistance (remember- the reciprocal of the sum of reciprocals), we can have a 3.33 Ohm resistor wired in parallel with a 5 Ohm resistor and still achieve an RT of 2 Ohms (technically 1.9988, close enough). See the formula below which breaks it down:
RT = 1 / (1/3.33 + 1/5) = 2
Feel free to work that out on a calculator if you're uncomfortable with it, but I assure you it will yield ~2. Also, for this example we will assume our voltage is still set to 5 volts. So far, we have the exact same RT and V as our previous example. As such, our total current IT will also be the same as our previous example. Once again, total current is equal to voltage times total resistance. This is illustrated again below for good measure.
IT = V / RT = 5/2 = 2.5 amps
Now that we are dealing with two coils of different resistances (R1 = 3.33, R2 = 5), the current will no longer be the same through each coil. We can prove this in the formulas below (note that voltage remains the same despite the varying resistance values):
IR1 = V/R1 = 5/3.33 = ~1.5 amps
Now we can do the same thing to IR2:
IR2 = V/R2 = 5/5 = 1 amp
Notice that once again, the two individual currents add up to the IT of 2.5 amps just like they did in the first example. Another thing to look at is the fact that since IR1 is not equal to IR2, PR1 will not be equal to PR2. This is illustrated below:
PR1 = V * IR1 = 5 * 1.5 = 7.5 watts
PR2 = V * IR2 = 5 * 1 = 5 watts
Once again, by adding these two values together you will find that our total power (PT) has not changed from the previous example, it is simply distributed differently. Now, continue below to see some practical uses for all of this information!
DUAL COIL VS. SINGLE COIL
Now that you have a basic understanding of Ohm's Law as it relates to dual coil devices, some practical conclusions can be drawn in regards to dual coil vs. single coil. For starters, let's talk about power consumption of single coil devices versus dual coil devices. First assume we are now using a 2 ohm single coil delivery device, and our PV is now set to 4 volts. Using Ohm's Law, we can determine the current and wattage. See below for equations and answers:
First, solve for current:
I = V / R = 4 / 2 = 2 amps
Now that we know the current, we can solve for power:
P = V * I = 4 * 2 = 8 watts
Assume that with these settings, you find that your vaping experience is quite pleasant. You then remove your single coil device and put your 2 ohm dual coil device on your PV. You still have the PV set to 4 volts. You then take a draw from your e-cig, only to find that your vapor production is actually not any better than it was on the single coil! This is because instead of having 8 watts pumping through a single 2 ohm coil, you now have 8 watts divided up evenly between two 4 ohm coils. In other words, you now have 2 coils set at 4 watts each.
The power gets divided up between these coils because the current gets divided up between these coils. The total current IT of 2 amps is going to be the same as it was with the single coil delivery device due to the fact that our PV is still set to 4 volts and it is still reading our delivery device total resistance as 2 ohms. However, now that you have two coils this current gets divided up between them. In other words, each coil is now only receiving 1 amp.
So what does this all mean?
If you are vaping on a dual coil device in the hopes of achieving double vapor production, you will have to double the power output of your PV. Remember that we enjoyed vaping at 8 watts through a single coil. If we are using a dual coil device and want to push 8 watts through each coil, our PV will have to be set to output 16 watts (*Note that some PVs will not allow a power output this high but stick with me here). Not everyone uses variable wattage devices though, so we need to determine which voltage setting would yield the equivalent of 16 watts so that we can achieve 8 watts through each coil.
First of all, we know that we want 8 watts through each coil (PRT of 16 watts) and we know that each coil is 4 ohms (RT of 2 ohms). It just so happens that there is a formula we can use to determine the proper voltage based on these two numbers alone. See that equation below:
V = √ (PRT * RT) = √(16 * 2) = ~5.65 volts
In other words, if you have a variable wattage device you can simply double the wattage to achieve "double the vapor" from a dual coil device. If you have a variable voltage device, you can either do the math using an Ohm's Law calculator or simply vape to taste. Many people find that the do not need to actually double their power output to achieve desirable results from a dual coil device. Regardless of how you do it, increasing your power output will obviously deplete your battery charge quicker.
CONCLUSION
So, should you be using a dual coil device? That is entirely up to you. This thread was not intended to promote or demote dual coil devices, it was created simply to explain their operation and how they compare to single coil devices. That being said, many people enjoy dual coil devices and it is highly recommended that you at least try one.
In case you were wondering, this thread was created in response to a lively debate in a separate section of the forum wherein I was asked to share some of my knowledge on dual coils & Ohm's Law. I have Bachelor of Science in Electronics Engineering Technology and I'm very interested in the technology behind e-cigarettes. I can also respect the fact that similar posts may already exist; I just felt compelled to explain it in my own words. This concludes my explanation of Ohm's Law as it applies to dual coils. Hopefully this was at least comprehensible- just let me know if you have any questions or issues with it!
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