A uniform wire of length l and radius r has a resistance of 100 .  It is recast into a wire of radius \frac{r}{2} .  The resistance of new wire will be :

  • Option 1)

     1600 \Omega

  • Option 2)

     400 \Omega

  • Option 3)

     200 \Omega

  • Option 4)

     100 \Omega

     

 

Answers (2)

As we learnt in

Resistance formula -

R=\rho \frac{l}{A}=\frac{m}{ne^{2}\tau}\cdot \frac{l}{A}

- wherein

\rho = resistivity of material

n= Number of free electrons per unit volume.

 

 R= \frac{\rho l}{a}=\frac{\rho lA}{^{A^{2}}}=\frac{\rho V}{A^{2}}R= \frac{\rho l}{A}=\frac{\rho lA}{^{A^{2}}}=\frac{\rho V}{A^{2}}

R\propto \frac{1}{A^{2}}=R\propto \frac{1}{r^{4}}

\therefore \frac{R_{2}}{R_{1}}=16=R_{2}=16R_{1}=16\times 100

R_{2}=1600\Omega

 


Option 1)

 1600 \Omega

This solution is correct 

Option 2)

 400 \Omega

This solution is incorrect 

Option 3)

 200 \Omega

This solution is incorrect 

Option 4)

 100 \Omega

 

This solution is incorrect 

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