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If I have a heating wire with resistance $R$ to be connected across a constant potential difference $V$, it would seem like cutting the wire into two (thus each having half the resistance) and connecting both across the voltage gap would quadruple the power output according to $P = \frac{V^2}{R}$.

Why is this not such a good idea? I thought that it was because the current going through the wires would double, but that doesn't seem too bad. What actually makes this not such a good idea?

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  • $\begingroup$ Who says it is not a good idea? Only problem would be if the wires cannot handle the power and melt. $\endgroup$
    – KvdLingen
    Commented Mar 9, 2014 at 0:06
  • $\begingroup$ "not a good idea", you mean that it heats up fast? $\endgroup$
    – wonderich
    Commented Mar 9, 2014 at 0:13
  • $\begingroup$ the power would double $\endgroup$
    – mcodesmart
    Commented Mar 9, 2014 at 0:17
  • $\begingroup$ what do you mean by "doesn't seem too bad"? can you state it scientifically, instead of using emotional adjective? :-) $\endgroup$
    – wonderich
    Commented Mar 9, 2014 at 0:26
  • $\begingroup$ @MahderT: the power in each wire would double, but now you've got two wires. So it would quadruple, as OP said. $\endgroup$
    – chase
    Commented Mar 9, 2014 at 1:12

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Your logic is completely correct. Two 1/2 R resistors in parallel will dissipate 4x the power of a 1 R resistor at the same applied voltage.

Whether that is "good" or not depends on whether the wire can handle the extra heat, whether the power supply can supply the extra current, whether the extra heat is desirable, whether using the extra power is acceptable, etc. Clearly you haven't told us enough to be able to judge that.

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