A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10^{-8} m. What will be the length of this wire to make its resistance 10? How much does the resistance change if the diameter is doubled?

(a) From the given information,

Radius of wire, r =

Then area of cross-section will be,

Resistivity,

Resistance, R= 10

And, Length, L = (To be calculated)

Now, putting these values in the formula:

Thus, the length of copper wire required to make 10 resistance will be 122.5 meters.

(b) The resistance of a wire is inversely proportional to the square of its diameter. So, when the diameter of the wire is doubled (that is, made 2 times), then its resistance will become (one-fourth).

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