An electrical cable of copper has just one wire of radius $$9$$ mm. Its resistance is $$5$$ ohm. This single copper wire of the cable is replaced by $$6$$ different well insulated copper wires each of radius $$3$$ mm. The total resistance of the cable will now be equal to

Question

Infinity Learn · Accepted Answer

Let the resistance of single copper wire be .$$R1$$. If p is the specific resistance of copper wire, $$thenR1=$$ρ×$$lA1=$$ρ×l$$π$$$$r12$$………………(1)When$$ the wire is replaced by six wires, let the resistance of each wire be $$R2$$. $$ThenR2=$$ρ×$$lA2=$$ρ×l$$π$$$$r22$$………………$$(2)From$$ eqs. $$(1) and (2), we $$getR1R2=r22r12$$  or  $$5R2=3$$×$$10$$−$$329$$×$$10$$−$$32R2=45$$ΩThese six wires are in parallel. Hence the resistance of the combination would be $$R=456=7$$⋅$$5$$Ω

An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5 ohm. This single copper wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. The total resistance of the cable will now be equal to

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