Question

A given wire of resistance 1 ohms is stretched to triple its length,What will be the new

resistance?​

Answer 1

Answer:

Since the resistance of a wire is given by R = rho*l/A the length while cutting the cross-section by 3x, the new resistance will be 9 times the original resistance.

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Answer 2

Given: a wire of resistance 1Ωis stretched to double its length.

To find the new resistance

Solution:

Here,

R=1Ω,Length=L,Cross sectional area, CSA=A

The formula used is,

$\boxed{ \sf \: R = \rho \frac{L}{A} }$

$\sf \implies \: \rho \frac{L}{A} = 1$

Now ,

new length, L'= 3L

And new CSA' = A

So we have,

Volume of the wire= AL

Now after the act of stretching the volume remains constant.

$\sf \therefore \: AL=A'L' \\ \\ \sf \: AL=A'3L \\ \\ \sf \: A' = \frac{A}{3}$

Now the new resistance of the wire becomes

$\sf \: R_{new}= \rho \frac{ L'}{A'} \\ \\ R_{new}= \rho \frac{3 L}{ \frac{A}{3}} \\ \\ R_{new}= 9\rho \frac{ L}{A} \\ \\ \\ \\ \sf \: R_{new}= 9 \times R \: \: \: from \: eqn \: (1) \\ \\ \therefore \: new \: resistance \: is \: 9 ohm$