Question

A Copper wire has a diameter of 0.5mm and a resistivity of 1.6 x 10-^8 ohm -m . What will be the Length of this wire to make resistance of 10 ohm ? How much does it's resistance change if the diameter is doubled ? ☺️

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Answer 1

Answer:

Let length be l

$r = \frac{ \rho \: l}{a} \\ \\l = \frac{ ra}{ \rho} = \frac{10 \times 0.5ohm \times {10}^{ - 3}m }{1.6 \times {10}^{ - 8}m } \\ \\ l = \frac{50}{16} \times {10}^{5} m = 3125 \: kms$

Now when diameters is doubled or area is increased 4 times resistance will be 1/4 th , since it's reciprocal