Q9 of 126 Page 198

What length of a copper wire of cross-section area 0.01 mm2 will be needed to prepare a resistance of 1 kΩ? Resistivity of copper = 1.7 × 10–8 Ω m.

0.6km

Given,


Resistance of the wire, R=1000Ω


Resistivity of copper, = 1.7 × 10–8 Ω m


Area of cross-section, A=0.01 mm2=0.01×10-6 m2


Formula used,


The expression for the resistance, R, of a wire is



Where ρ is the resistivity, A is the area of cross-section and ‘l’ is the length of the wire.


Or the length of the wire for given area and Area of a cross section is,



Solution,


Substituting the values in eqn.2, we get the required length as,




Hence the length of the copper wire for the given resistance is 0.6km.


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