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Question

# Two uniform wires A and B are of same metal have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is

A
4Ω when the resistance of wire A is 4.25Ω
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B
5Ω when the resistance of wire A is 4Ω
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C
4Ω when the resistance of wire B is 4.25Ω
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D
5Ω when the resistance of wire B is 4Ω
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Solution

## The correct option is A 4Ω when the resistance of wire A is 4.25ΩGiven: Two uniform wires A and B are of same metal have equal masses. The radius of wire A is twice that of wire B. To find the total resistance of A and B when connected in parallelSolution:We know, mass=density × volume⟹m=d×πr2AlA=d×πr2BlB⟹lA=(rBrA)2lB=(rB2rB)2lB⟹lA=lB4Now substituting this value in equation R=ρlA⟹RA=ρlAπr2A,RB=ρlBπr2B⟹RA=ρlAπr2A,RB=ρ4lAπ(rA2)2=ρ16lAπr2Aor, RB=16RAHence, Rtotal=RARBRA+RB=RA×16RARA+16RA⟹Rtotal=4.25×16RA17RA=4Ωis the total resistance of A and B when connected in parallel.

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