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( 1):/RL=PL

Let the current flowing through R0 in the double-wire working state be I 1, then

I1r0+I1rl/2 = u (voltage shared by r0+voltage shared by two wires = voltage across the power supply, and the resistance of two wires in parallel is half that of a single wire).

Let the current flowing through R0 in the working state of monofilament be I2, then

I2R0+I2RL = U (shared voltage of R0+shared voltage of single filament = voltage at both ends of power supply)

The heat generated by working with a single filament is still the same as that generated by working with a double filament, then

2(I 1/2)? RL=I2? RL,I 1? /I2? =2

Get r0 = √ 2/2 ul? /PL

(2): Let R0 be the ratio of power consumed by single-line operation and double-line operation, k.

k=I 1? R0/I2? R0=I 1? /I2? =2