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Question

A wire of 3 ohm resistance and 10 cm length is stretched to 30 cm length. Assuming that it has a uniform cross section, what will be its new resistance?

A
27Ω.
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B
9Ω.
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C
3Ω.
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D
30Ω.
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Solution

The correct option is A 27Ω.
On stretching a wire, both its area of cross-section and length changes but its volume remains constant.

R1=3Ω , l1=10cm , l2=30cm=3l1

And, A=Vl

Now, R=ρlA

R=ρl2V

Rl2

On increasing length to 3 times of initial value.
Hence, R2R1=l22l21=9

R2=9R1=9×3Ω

R2=27Ω

Answer-(A)

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