Where is most of the power being used? What does that tell you about how the load resistance compares to the copper wire resistance? And what does that say about the effect on the current of making the wires a bit thinner?songoku said:
In the heating element of the ovenharuspex said:
The load resistance is higher than the copper wire resistanceharuspex said:
Making the wires a bit thinner will increase the resistance of the wire and also the total resistance of the circuit so the current will decreaseharuspex said:
That would mean your roast isn't roasted any more (but slow-cooked instead) !songoku said:
You might like to try some simple calculations which should make it clear.songoku said:
Sure, but I asked how the two resistances compare. If you double the resistance of the copper wires, how much difference will that make to the total resistance? How much will the current drop?songoku said:
$$\frac{P_{oven}}{P_{cable}}=\frac{R_{oven}}{R_{cable}}$$BvU said:
From calculation I got the power actually doubles when the resistance of the wire doubles.Steve4Physics said:
Doubling the resistance of the copper wires will make the total resistance to be ##2R_c+R_o## (where ##R_c## and ##R_o## are the resistance in cable and oven respectively). So the ratio between the initial total resistance and the new total resistance is ##\frac{R_o + R_c}{2R_c + Ro}##haruspex said:
$$P_t=\frac{V^2 ~ r_t}{(r_t+R_o)^2}$$erobz said:
songoku said:
Well done. For ease of reference, here is the Post #5 question/answer:songoku said:
See if this helps.songoku said:
Exactly ! Or, if you want: $$P_\text {cable} = \frac {P_\text{oven}} {R_\text{oven}} \; R_\text {cable}$$ So -- with a given power as desired in the oven, and a given ##R_\text {oven}## -- you can minimize ##P_\text {cable}## by minimizing ##R_\text {cable}##songoku said:
The type of wire needed to prevent overheating is determined by factors such as the current-carrying capacity (ampacity), the wire gauge (thickness), the material of the wire (copper or aluminum), the insulation type, and the ambient temperature where the wire will be used.
Wire gauge affects overheating because thicker wires (lower gauge numbers) can carry more current without overheating. Thinner wires (higher gauge numbers) have higher resistance and can overheat if too much current flows through them. Therefore, selecting the correct gauge for the expected current load is crucial.
Copper wire is preferred over aluminum for preventing overheating because copper has a higher electrical conductivity, meaning it can carry more current with less resistance. This results in less heat generation compared to aluminum wire, which has higher resistance and is more prone to overheating under the same conditions.
Insulation plays a critical role in preventing wire overheating by providing a protective barrier that helps contain the heat generated by the wire. Proper insulation ensures that the heat does not escape and affect surrounding materials, reducing the risk of fire. Additionally, insulation materials are rated for different temperature ranges, so choosing the right type is essential for safety.
Ambient temperature impacts wire selection because higher temperatures can reduce the current-carrying capacity of a wire. In hotter environments, wires may need to be derated, meaning they are required to carry less current than their maximum capacity to avoid overheating. Therefore, it's important to consider the ambient temperature when selecting a wire to ensure it can handle the expected current load without overheating.
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