Question

The write of length L and resistance R istretched so that it's radius of cross-section is halved. What it's new resistance

Answer 1

Answer:

As we all know,

=> $R = \rho\frac{l}{A}$

This means that resistance is inversely proportional to area of cross section (A)

=> If the are is halved the the resistance is increased by 2 times

=> $R_{1} = \rho\frac{l}{A}$

When is the area of cross section is halved

=> $R_{2}=\rho\frac{l}{\frac{A}{2} } = \rho \frac{2l}{A}$ ( New resistance)

Now , $\frac{R_{1}}{R_{2}}$ gives

=> $\frac{R_{1}}{R_{2}} = \frac{\rho\frac{l}{A} }{\rho\frac{2l}{A} }$

=> $\frac{R_{1}}{R_{2}}=\frac{1}{2}$

=> $R_{2}=2R_{1}$

Therefore New resistance = 2( Original Resistance)

Hope You understood the concept.

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