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If we keep the voltage in a circuit constant, then $$H = \frac{V^2}{R}t$$ so if I increase the resistance, the current must decrease and so the heat will be less. Then why can't we use very good conductors, like copper, for heat formation?

I tried finding an answer in other Stack Exchange questions, but they all just explained why heat becomes less. Why do we use resistors like nichrome for heater coils?

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Because the voltage source and the rest of the circuit has some internal resistance. Therefore if you decrease the resistance of your consumer the voltage across your consumer will decrease, so there will be less heat created in your consumer.

Let $R_c$ be the resistance of your consumer and $R_i$ the internal resistance, then we have $$U_c=R_c I $$ $$U_i=R_i I $$ $$U=(R_c+R_i)I$$ and therefore $$P_c=R_cI^2=\frac{R_c}{(R_c+R_i)^2}U^2$$ the maximum of this function with respect to $R_c$ is $$R_c=R_i$$

Therefore you get the maximum heat dissipation in your consumer if your resistance matches the internal resistance of the circuit. Note however that this is inefficient, as the power dissipated in your internal resistance is equal to the power dissipated in your consumer (where you want the heat to be.) The quotient of consumer power to internal power loss is $$\frac{P_c}{P_i}=\frac{R_c}{R_i},$$ so the higher your consumer resistance is the more efficient it becomes. Therefore in reality you choose the resistance of your consumer much larger than the internal resistance to make the circuit energy efficient. Then you need a power source with high enough voltage so that you can still match the desired heat output.

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  • $\begingroup$ but why wouldn't a circuit with just copper wire heat up like a heater ? $\endgroup$ Feb 10, 2022 at 14:44
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    $\begingroup$ @HemantKumar Of course the copper wire will heat up. However you will have large a current since there is only low resistance in your circuit. This will also be inefficient since the copper wire outside your heater will heat up by the same amount. If you have a large resistor in your circuit then the copper wire will heat up much less since the total current is much lower. $\endgroup$
    – Azzinoth
    Feb 10, 2022 at 15:33
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Nichrome's main advantage is oxidation protection actually.

Let’s consider our toaster with two alternatives, copper for less resistance and graphite rods for higher resistance.

Both of them will oxidize at the temperature required to make a toast.

Copper will also be very complicated to feed. It will require a low voltage, but a high current. Even one continuous wire will not get enough resistance to connect directly into the mains. And a thinner wire will just burn faster.

With a graphite rod it is the reverse. The resistance is so high, that we would need to connect every rod in parallel to reduce the resistance sufficiently to use with the mains. And a thicker rod will just crack from internal forces after being heat cycled.

Our losses in main's wires are just a few percents all the way to the power plant, not worth the change.

So it all comes down to the cost and practicality. We use our mains voltage because history decided so. We use nichrome, because it doesn’t oxidize as easily.

Could we use high voltage mains in a new ideal world? I think yes. Probably 10 kV would be better, with a current limiter being used to quickly shut it down in case of an emergency.

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    $\begingroup$ I run a lab where we routinely have voltages at or above 10kV, and no (NO!), that would not be a good thing in your house. $\endgroup$
    – Jon Custer
    Feb 9, 2022 at 14:13
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    $\begingroup$ At 35 kV it punches right though 2 mm Teflon (e.g., using the wrong cable). First-hand experience. (2 mm if I remember correctly.) $\endgroup$ Feb 9, 2022 at 19:53

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