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A uniform wire resistance 100(Omega)is m...

A uniform wire resistance `100(Omega)`is melted and recast in a wire of length double that of the original . What would be the resistance of the wire?

Text Solution

Verified by Experts

`l = 2l Volume of wire remains constant
Ai = A' I' `
` rArr Ai = A' xx 2i `
` rArr A' = A/2 `
rho rArr Specific resistance `
` R = rhol/A' `
` R_1= rhol/A = 100 Omega `
` = (rho 2l/A/2) = (4rhol /A) = 4R`
` = 4 xx 100 Omega = 400Omega ` .
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Knowledge Check

  • A wire has a resistance of 32Omega . It is melted and drawn into a wire of half of its original length. What is the resistance of the new wire?

    A
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    B
    `16Omega`
    C
    `8Omega`
    D
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  • If the length of the metallic wire is doubled, then the resistance of the wire

    A
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    B
    doubles
    C
    reduces by `(1)/(4)`
    D
    quadruples

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    A
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    B
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    C
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    D
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