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Question

# The lengths of two wires made of same material are 2 m and 1 m.Their radii are 1 mm and 2 mm. The ratio of their specific resistances is:

A
2 : 1
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B
1 : 2
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C
4 : 1
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D
1 : 1
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Solution

## The correct option is B 2 : 1Given that, Length of the wire l1=2m Length of the wire l2=1m Radii of the wire r1=1mm Radii of the wire r2=2mm We know that, R=ρlA Now, the specific resistances for both wires R1=ρ1l1A1 R2=ρ2l2A2 As material is same of both wires So, R∝lA Where, A=πr2 Now, the ratio of specific resistance is R1R2=ρl1×A2ρl2×A1 R1R2=1×r222×r21 R1R2=1×42×1 R1R2=21 Hence, the ratio of specific resistance is 2:1

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