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Wire Gauge and Resistance problem

I am using 18 gauge nicrome wire having ohm of 17.3 , 220 volt. I want to use 10 gauge wire how to decide the length?

Padmanava asked

Answer:

18 gauge corresponds to a diameter of 1.22 mm

Therefore radius r1= 1.22/2=0.61 mm=0.00061m

10 gauge means diameter is 3.25 mm

Radius r2 = 3.25/2=1.625mm=0.001625m

Sine the resistance needs to be the same, we can use the formula

$\LARGE \bg_white R=\frac{\rho l}{A}$
Which gives
$\LARGE \bg_white \frac{l_{1}}{A_{1}}=\frac{l_{2}}{A_{2}}$
As resistivity is same.

$\LARGE \bg_white l_{2}=\frac{l_{1}A_{2}}{A_{1}}=\frac{l_{1}r_{2}^{2}}{r_{1}^{2}}$

Substitute the values and you will get the answer.

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