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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 m2Given that Resistivity,? = 1.6 x 10?m Resistance,R = 10 ? We have to calculate the length. We have Resistivity, ?= R x A / li.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 mThus,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) |