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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 : 1

Given 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, RlA

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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