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# what is the relation among them? Answered

hi my good friends
want to ask a simple question
i want to make an electric heater.
what is relation between wire length and gauge of nichrome wire for use in heaters. how gauge and length of wire can effect the efficiency of heater output.
is there any other wire that have more heating output than nichrome wire?
thanks all and love u

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With a heater, power in= power out. They are 100% efficient at converting electrical energy into thermal.

Now, how much power do you want ?

The longer a wire the greater the resistance.

The thinner the wire the greater the resistance.

The bigger the AWG wire gauge the greater the resistance.

The hotter the wire the greater the length and greater resistance.

This applies to toaster wire that is often flat.. Where the smaller the cross sectional wire area the greater the resistance.

In designing electric heaters you must consider the mains voltage, the wire resistance which is a function of the wire composition and tables which describe the temperature based on the current flowing through the wire

Amperes = Voltage / Resistance (when hot)

Support of the wire is very important because it will try to sag when lengthened by heat and could touch something it should not.. That is why this wire is often loop coiled between supports to stay in a stable position or strung through insulating high temperature stable insulation as in a toaster..

Wire used for making heating elements is called resistance wire.

https://en.wikipedia.org/wiki/Resistance_wire

Resistance wire is usually made of some metal alloy that can withstand high temperatures and being surrounded by an oxidizing atmosphere. Nichrome is one well known example. Kanthal is another.

https://en.wikipedia.org/wiki/Nichrome

Actually nichrome is so well known that I have overheard that word used as the hypernym; e.g. saying "kanthal is kind of nichrome", which is untrue.

It is sort of like saying that corn chips are a kind of potato chips, or pretzels are a kind of potato chips. It is like the speaker strangely thinks that every kind of salty snack food is called, "potato chips".

Anyway, the trick to building a heating element from resistance wire is to think of your heating element as a resistor.

It also helps to have a target for the amount of power, as heat, measured in watts, that you want your heating element to dissipate.

From Ohm's law, the power dissipated by a resistor is just

P = V*I = V^2/R = I^2*R

It also helps to know to consider the power source driving your heating element, and to model it as a voltage source in series with a small internal resistance. This is the same thing as a Thevenin equivalent power source,

https://en.wikipedia.org/wiki/Th%C3%A9venin%27s_th...

The reason why it is convenient to think of it this way, is because then you have a circuit with just two resistors in series. One is your heating element. The other is the internal resistance of your power supply.

The reason this internal series resistance, Rs, is important to think about, is because it is likely the only place where you can loose, or waste, power. Call the other resistor, your heating element, Rh.

Because Rs and Rh are in series, they share the same current I. Power dissipated in the heating element is

Ph = I^2*Rh

Power lost to heating the series resistance in the power supply is

Ps = I^2*Rs

The moral of this story is you want to make Rh, the resistance of your heating element, much larger than Rs, the series resistance of the power supply. E.g. make Rh ten times the size of Rs, Rh =10*Rs

and Ph/(Ph+Ps) = 10/11 = 0.9090

and 91% of your power goes into the heating element

(and 9% is lost heating the power supply)

For actually calculating the resistance of a length of wire, with some given length L, and cross section area A, and bulk resistivity rho (a characteristic of the metal itself), there is the general formula

R= rho*L/A

Although for nichrome wire, or kanthal wire, etc. you probably won't have to use that formula, because there are tables and stuff, that can tell you the resistance per unit length (e.g. ohm/m) for a particular thickness (called gauge, or AWG) for a particular kind of wire (e.g. nichrome, kanthal, etc)

Also there may be a correction for temperature, but usually this is small. Like for nichrome it is like a difference of only 10% smaller at red hot, like 1000 C, versus the resistance at room temperature.