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Q. A wire of resistance R is uniformly stretched until its radius is halved. Its new resistance is

KCETKCET 1999Current Electricity

Solution:

As we know,
$ R =\frac{ \rho L }{ A } . $
If you stretch the wire till it's radius is halved the previous value, then it's length will increase 4 times to keep the volume constant.
So, new values are,
$ \begin{array}{l} L _2=4 L \\ A _2=\frac{ A }{4} \end{array} $
where, $L$ and $A$ are the values of original length and area
Resistivity remains the same as it depends upon the material of the wire. So, the new resistance will be,
$ \begin{array}{l} R _1=\frac{\rho L }{ A } \\ R _1=\frac{\rho 4 L }{ A / 2} \\ R _1=\frac{16 \rho L }{ A } \\ R _1=16 R \end{array} $