How a heating element is connected to increase power

In summary: Gold, sulphur and arsenic...interesting alternatives, what physical properties of these elements make you suggest them?Gold is too expensive and too conductive - but provides a good electrical connection.Sulfur is too resistive.Arsenic begins to sublimate at 615C and would not be a good choice because it might not be available in the heating element.
  • #1
moenste
711
12

Homework Statement


An electrical heating element is to be designed so that the power dissipated will be 750 W when connected to the 240 V mains supply.

(a) Calculate the resistance of the wire needed.

(b) The element is to be made from nichrome ribbon 1.0 mm wide and 0.050 mm thick. The resistivity of nichrome = 1.1 * 10-6 Ω m. Calculate the length of ribbon required.

(c) Draw a circuit diagram to show how a second heating element would be connected to increase the power dissipated to 1.5 kW.

(d) State one important property of a conductor used to make heating elements.

Answers: (a) 76.8 Ω, (b) 3.49 m.

2. The attempt at a solution
(a) P = V * I and R = V / I. So we find I = P / V = 750 / 240 = 3.125 A and find R = 240 / 3.125 = 76.8 Ω.

(b) Area = (1 / 10 / 100) * (0.050 / 10 / 100) = 5 * 10-8 m2. L = (R * A) / ρ = (76.8 * 5 * 10-8) / (1.1 * 10-6) = 3.49 m.

(c) This is the part I'm not sure. This is how I see the question:

d436c2931327.jpg


I would say that if we add another 76.8 Ω heating element the current would increase to 6.25 A (1500 W / 240 V). And then I just put the second element above or beneath the given one. And then we will have a series circuit with I = 6.25 A, two elements with R = 76.8 Ω each and V = 240 V. Is this correct?

(d) This thing I don't know. Maybe it has to do something with it's dimensions or resistivity or something else?
 
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  • #2
moenste said:
And then we will have a series circuit with I = 6.25 A, two elements with R = 76.8 Ω each and V = 240 V. Is this correct?
Are you sure it is a series circuit?
 
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  • #3
If you wanted two 750 watt elements to generate 1.5KW, would you hook them up in series?
Would nichrome ribbon be a better heating element than copper? murcury? sodium?
 
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  • #4
moenste said:
a series circuit
?
 
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  • #5
cnh1995 said:
Are you sure it is a series circuit?

.Scott said:
If you wanted two 750 watt elements to generate 1.5KW, would you hook them up in series?
"Cokes ... 1, 2, 3, 4, ..."
 
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  • #6
cnh1995 said:
Are you sure it is a series circuit?
.Scott said:
If you wanted two 750 watt elements to generate 1.5KW, would you hook them up in series?
Ah, yes, they should be done in parallel. We can check it by: V = 240 V, I = 6.25 A so R = 240 / 6.25 = 38.4 Ω total resistance of the circuit. And this goes in hand with 1 / R = 1 / 76.8 + 1 / 76.8 → R = 38.4 Ω.

.Scott said:
Would nichrome ribbon be a better heating element than copper? murcury? sodium?
No idea on this topic. What should be of particular interest in analyzing this?

Bystander said:
"Cokes ... 1, 2, 3, 4, ..."
Cokes?
 
  • #7
moenste said:
Cokes?
Simultaneous, or nearly so, responses that are so similar as to be indistinguishable, in the days of the dinosaurs was followed immediately with a chorus of "Cokes (the beverage) and some locally agreed upon enumeration (the count)."
 
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  • #8
Bystander said:
Simultaneous, or nearly so, responses that are so similar as to be indistinguishable, in the days of the dinosaurs was followed immediately with a chorus of "Cokes (the beverage) and some locally agreed upon enumeration (the count)."
Alright, looks like (c) is solved : ).

Any suggestions on this part:
moenste said:
(d) State one important property of a conductor used to make heating elements.
?
 
  • #9
What's the most relevant property?
 
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  • #10
Bystander said:
What's the most relevant property?
Maybe current?
 
  • #11
Current is not really a property of conductors, since it does vary with voltage; you're so close.:nb)
 
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  • #12
Bystander said:
Current is not really a property of conductors, since it does vary with voltage; you're so close.:nb)
Maybe resistance? It should not vary with voltage.
 
  • #13
Closer.
 
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  • #14
Bystander said:
Closer.
It should be resistivity of the material, right?
 
  • #15
moenste said:
resistivity
:partytime:
 
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  • #16
Bystander said:
"Cokes ... 1, 2, 3, 4, ..."

Don't you mean 4,3,2,1,...cokes ?
 
  • #17
Would nichrome ribbon be a better heating element than copper? mercury? sodium?
moenste said:
No idea on this topic. What should be of particular interest in analyzing this?
That was my attempt to help you with that last question.
Copper isn't very resistive. Mercury is a liquid in most heating applications. Sodium is pretty reactive.
How about gold, sulfur, arsenic?
 
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  • #18
.Scott said:
Would nichrome ribbon be a better heating element than copper? mercury? sodium?

That was my attempt to help you with that last question.
Copper isn't very resistive. Mercury is a liquid in most heating applications. Sodium is pretty reactive.
How about gold, sulfur, arsenic?

Gold, sulphur and arsenic...interesting alternatives, what physical properties of these elements make you suggest them??
 
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  • #19
lychette said:
Gold, sulphur and arsenic...interesting alternatives, what physical properties of these elements make you suggest them??
Gold is too expensive and too conductive - but provides a good electrical connection. Sulfur is too resistive. Arsenic begins to sublimate at 615C and would produce AsO3 before that - either would be very toxic.
So you want something that is solid, inexpensive, resistive, but not an insulator, non-corrosive, not lethal, etc. All properties of a good heating element.
Also, ideally it would become more resistive as the temperature increased.
 
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  • #20
.Scott said:
Would nichrome ribbon be a better heating element than copper? mercury? sodium?

That was my attempt to help you with that last question.
Copper isn't very resistive. Mercury is a liquid in most heating applications. Sodium is pretty reactive.
How about gold, sulfur, arsenic?
Nichrome (specific resistance / resistivity): 1.1 * 10-6 Ω m
Copper: 17 * 10-9 Ω m
Mercury: 960 * 10-9 Ω m
Sodium: 47 * 10-9 Ω m
Gold: 22 * 10-9 Ω m
Sulfur: 1 * 1015 Ω m
Arsenic: 3 * 10-7 Ω m

So the higher is the resistivity of an element, the better it fits for the purpose of a heating element? In case we don't consider things like cost, toxication, melting properties and so on like in this question.

And it looks like sulfur has the largerst resistivity, so solely based on this property it is a good fit?
 
  • #21
lychette said:
Gold, sulphur and arsenic...interesting alternatives, what physical properties of these elements make you suggest them??
I was trying to introduce problematic choices - to assist with an answer to that OP's question #4. In each case, there is a reason that these are not good choices. So, each demonstrates a potential answer to question 4.
 
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  • #22
moenste said:
Nichrome (specific resistance / resistivity): 1.1 * 10-6 Ω m
Copper: 17 * 10-9 Ω m
Mercury: 960 * 10-9 Ω m
Sodium: 47 * 10-9 Ω m
Gold: 22 * 10-9 Ω m
Sulfur: 1 * 1015 Ω m
Arsenic: 3 * 10-7 Ω m

So the higher is the resistivity of an element, the better it fits for the purpose of a heating element? In case we don't consider things like cost, toxication, melting properties and so on like in this question.

And it looks like sulfur has the largerst resistivity, so solely based on this property it is a good fit?
As I said in an earlier post, sulfur is too resistive - it's basically an insulator. In order to get it to carry significant current and thereby generate significant heat, you would need to apply a very high voltage.
 
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  • #23
.Scott said:
As I said in an earlier post, sulfur is too resistive - it's basically an insulator. In order to get it to carry significant current and thereby generate significant heat, you would need to apply a very high voltage.

If the resistance of the heater is halved then the current is doubled (assuming same voltage power supply).
This means that the power is doubled...doesn't this suggest that lower resistivity is an advantage?
 
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  • #24
It's not only the electrical properties that matter .

The element material has to have a high melting point , adequate mechanical strength and be resistant to oxidation ..

The material also has to be workable .
 
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  • #25
Nidum said:
It's not only the electrical properties that matter .

The element material has to have a high melting point , adequate mechanical strength and be resistant to oxidation ..

The material also has to be workable .
I may be wrong here but does 'specific heat' count? Would 'lower specific heat' be a desirable property for a heating element?
 
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  • #26
lychette said:
If the resistance of the heater is halved then the current is doubled (assuming same voltage power supply).
This means that the power is doubled...doesn't this suggest that lower resistivity is an advantage?
It could be. But let's say you divided it by 100. The current would increase by a factor of 100 and the entire circuit would burn itself out.
In general, you are looking for a specific heat output for your heating element. So if you used a material of lesser resistance, you could use a thinner or longer piece to get the same resistance and therefor the same power (heat) output. But if you pick something with very low resistance, this can get to be a problem. If it is too long and this, it may be too fragile.
 
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  • #27
cnh1995 said:
I may be wrong here but does 'specific heat' count? Would 'lower specific heat' be a desirable property for a heating element?
Specific heat could be important. It would affect how much energy is required to heat up the filament itself. Combined with the thermal conductivity, it would help keep the entire filament at one temperature. This is important because a small defect in one part of the filament could make that spot more resistive and therefore generate more heat. So a small defect can overheat causing a larger defect causing more heat, etc. Keeping the filament at the same temperature keeps these defects from growing as quickly.
 
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  • #28
.Scott said:
It could be. But let's say you divided it by 100. The current would increase by a factor of 100 and the entire circuit would burn itself out.
In general, you are looking for a specific heat output for your heating element. So if you used a material of lesser resistance, you could use a thinner or longer piece to get the same resistance and therefor the same power (heat) output. But if you pick something with very low resistance, this can get to be a problem. If it is too long and this, it may be too fragile.

What do you mean by "specific heat output"... The original post refers to "power"
You cannot be sure that increasing the current by a factor of 100 would 'burn out the entire circuit' without more details.

The principals are what matters
 
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  • #29
lychette said:
What do you mean by "specific heat output"... The original post refers to "power"
You cannot be sure that increasing the current by a factor of 100 would 'burn out the entire circuit' without more details.

The principals are what matters
True enough. In the original circuit, we started out generating 750W. Reducing the resistance by 100 has the potential of generating 75KW. Assuming your original 240-volt power source was capable of generating 75KW, your 3.49 meter long, 1.0mm wide ribbon would now be dissipating heat at about 215 watts per centimeter. So, "burn out the entire circuit" was inaccurate. Perhaps you trip a breaker. Perhaps you detonate your filament. Perhaps you burn out your 240V generator. Perhaps you do all three. I only meant to communicate the notion of "something bad happens".
 
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1. How does a heating element increase power?

A heating element is typically connected to an electrical circuit, which provides the power needed to heat up the element. When electricity flows through the element, it encounters resistance, which causes the element to heat up. The higher the resistance, the more power is needed to generate heat.

2. What type of connection is used to increase power to a heating element?

A heating element is typically connected in a series circuit, where the electricity flows through the element and then continues on to the rest of the circuit. This allows for the full voltage of the circuit to be applied to the element, increasing the power and heat output.

3. Can multiple heating elements be connected to increase power?

Yes, multiple heating elements can be connected in a series or parallel circuit to increase power. In a series circuit, the resistance of each element adds up, resulting in a higher overall resistance and increased power. In a parallel circuit, each element receives the full voltage of the circuit, resulting in a higher power output.

4. Are there any safety concerns when connecting a heating element to increase power?

Yes, it is important to ensure that the heating element is properly rated for the increased power load. Using an element with a lower resistance than the circuit is designed for can lead to overheating and potentially cause a fire. It is also important to follow proper wiring and circuit protection guidelines to prevent electrical hazards.

5. What factors can affect the power output of a heating element?

The power output of a heating element can be affected by the voltage and current of the electrical circuit it is connected to, as well as the resistance of the element itself. Other factors such as the material and design of the element, as well as ambient temperature, can also impact the power output. It is important to consider all of these factors when designing a circuit with a heating element to ensure safe and efficient operation.

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