Ask a Teacher



A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10 raise to -8 ohm meter . what will be the length of this wire to make its resistance 10 ohm? How much does the resistance change if the diameter is doubled?

Given that the diameter of the copper wire is 0.5 mm
Therefore , radius of the wire , r = 05 / 2 = 0.25 mm
i.e., radius ,r = 025 x 10-3 m
Area of cross section of the wire,A = ?r2

                                                   = 22/7 x (0.25 x 10-3)2

                                                   = 0.1964 x 106 m2

Given that Resistivity,? = 1.6 x 10?m

              Resistance,R = 10 ?

We have to calculate the length.

We have Resistivity, ?= R x A / l

i.e;  1.6 x 10-8 = 10 x 0.1964 x 10-6 / l

                     l = 10 x 0.1964  x 10-6 / 1.6 x 10-8

                    l = 122.7 m

Thus,the length of copper wire required to make 10? resistance will be 122.7 metres.

The resistance of a wire is inversely proportional to the square of its diameter.So, when the diameter of the wire is doubled .then its resistance will become  (1/2)2 or 1/4(one- fourth)