Q15 of 19 Page 12

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? ( CBSE 2009, 2006)

(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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