Calculations

Increasing Resistance

 
I have a 12v 10Ah Battery, but I only want a 18 inch straight wire cutter at 600°F.
You may also consider that you have a 12v 3a Solid state DC Power Supply

Because you know that you want a straight wire cutter, you’ll be dealing with 24 or 26 gauge NiChrome Wire. For this example, we’ll use 26 gauge, which requires around 2 amps to heat to 600°F
1.) Determine the required high and low ratings of your circuit.
You may choose to use Jacobs Online Calculator, or proceed manually.
See the Battery Section for a walk through on the calculator.

      HIGH TEMP
Total Required Resistance (Rt) = Power Source Voltage / Required Amperage
Rt = 12 / 3.2
Rr = 3.75 ohms

Resistor Wattage Rating (Wr) = Required Amperage^2  x  Resistor Resistance
Wr = I^2  *  Rr
Wr = 3.2^2 * 3.75
Wr = 38.4 Watts


      LOW TEMP
Total Required Resistance (Rt) = Power Source Voltage / Required Amperage
Rt = 12 / 1.67
Rr = 7.2 ohms

Resistor Wattage Rating (Wr) = Required Amperage^2  x  Resistor Resistance
Wr = I^2  *  Rr
Wr = 1.67^2 * 7.2
Wr = 20.1 Watts

From these two results, take the highest wattage, and the highest resistance
:: Rheostat Rating ::
38.4 Watts  &  7.2 Ohms
By taking the highest resistance you can ensure a low temperature, and the highest wattage allows for the most power absorption by your rheostat.

To continue on with this tutorial, we’ll assume you were only
able to find a 50 Watt, 6 Ohm resistor



2.) Calculate the Resistance of the NiChrome Wire
Rn = 2.67 ohms/foot * 1.5 feet
Rn = 4 ohms


3.) Calculate the Resistance required for 600°F
Circuit Resistance (Rc) = Power Source Voltage / Required Amperage
Rr = 12 / 2
Rr = 6 ohms

4.) Calculate the required set resistance of your rheostat
Set Rheostat Resistance = Circuit Resistance - NiChrome Resistance
Rr = Rc - Rn
Rr = 6 - 4
Rr = 2ohms

5.) Calculate how far the rheostat dial needs to be set (just a percentage)
Rr / Rc
2 / 6
33% rheostat activation


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The wattage rating is how much energy the resistor can absorb. Use the highest calculated wattage rating.

It is more important to have an accurate Ohm rating for your resistor than it is the wattage.

Rheostats

In addition to this added control, you can use rheostats to increase the resistance of your circuit if you have one source of power, but want to change between cutting devices.

When dealing with resistors and rheostats, there are a few points to keep in mind...

Consider the Wattage rating is a minimum,

and the Ohm rating is a maximum.

EXAMPLE

One difference when calculating a rheostat in comparison to a resistor, is that with a rheostat you will require a range of resistances that correspond to the temperature of your wire.

At this point, you should know that the current flowing through your wire produces heat, and the amount of current is dependent upon circuit resistance and the voltage of your supply.

As a rule of thumb, I recommend calculating resistances at 400°F and 1000°F.

That way when your rheostat is turned off, it will provide no resistance, and the maximum current will be pulled through your NiChrome Wire (to produce a temperature of 1000°F). But when the rheostat is turned completely on, it will provide maximum resistance, and the lowest current and coolest temperature will be provided.

You can set the high and low temperatures at whatever you choose, just know that you need to choose the appropriate amperage ratings for your gauge NiChrome Wire.

Although, it is best to choose a high temperature and high amperage that corresponds to the highest rated safe current from your power source.

You will need to perform this calculation twice, for the high and low amperage.

With all of these calculations, you are able to determine that with a 18” cutter you need to have the dial set at 33% activation.


But if you want to change to a 6” cutter, the dial will have to be set different. Just repeat steps 2 - 5.

2.) Calculate the Resistance of the NiChrome Wire (6 inches)

Rn = 2.67 ohms/foot * 0.5 feet

Rn = 1.3 ohms



3.) Calculate the Resistance required for 600°F

Circuit Resistance (Rc) = Power Source Voltage / Required Amperage

Rr = 12 / 2

Rr = 6 ohms


4.) Calculate the required set resistance of your rheostat

Set Rheostat Resistance = Circuit Resistance - NiChrome Resistance

Rr = Rc - Rn

Rr = 6 - 1.3

Rr = 4.7 ohms


5.) Calculate how far the rheostat dial needs to be set (just a percentage)

Rr / Rc

4.7 / 6

78% rheostat activation

So NOW you see that for a 18” cutter the dial has to be set to 33% and then if you want to change to a 6” cutter you need to set the dial to about 75%.

This is the reason why we calculate the high & low rheostat ratings, so that you can switch between cutting devices and be able to have a safe rheostat rating...!

Rather than try to explain any more, it would probably be best to read through the example below, so that you can see how a rheostat is calculated and how it is applied to a circuit.

They’re really cool..!

Conceptually calculating rheostat is not that much different than a resistor, but it is rather advanced  and may not be easy for everyone. Definitely at this point if you have not yet visited the Circuit Theory Page, then visit the Resistor Page before proceeding further.

You may notice that this is similar to the Resistor Section, because it is.. The only difference is that resistors cannot be altered and have a fixed resistance rating.

Visit the Fixed Voltage Power Section for more information on this topic as many concepts overlap.

Rheostats (also known as Potentiometers) are a wire wound variable resistor which you can apply to a circuit that has a fixed power supply. In doing so you can control the temperature of a fixed voltage power supply, or a battery, without actually having to change the NiChrome Wire length. They’re really handy for those that have a little know-how of electrical circuitry.

General Discussion
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