A material  B  has twice the specific resistance of  A . A circular wire made of B  has twice the diameter of a wire made of A. Then for the two wires to   have the same resistance, the ratio l_{B}/l_{A}     of their respective lengths must be      

  • Option 1)

    2

  • Option 2)

    1

  • Option 3)

    1/2

  • Option 4)

    1/4

 

Answers (2)

As we learnt in

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

- wherein

\rho\rightarrow  resistivity / specific resistance

 

Resistance of a wire  R= \frac{\rho l}{\pi r^{2}}= \frac{\rho l\times 4}{\pi D^{2}}

\because R_{A}= R_{B}

\therefore \frac{4\rho _{A}l_{A}}{\pi D_{A}^{2}}= \frac{4\rho _{B}l_{B}}{\pi D_{B}^{2}}

\frac{l_{B}}{l_{A}}= \left ( \frac{\rho _{A}}{\rho _{B}} \right )\left ( \frac{D _{B}}{D _{A}}\right )^{2}

= \left ( \frac{\rho _{A}}{2\rho _{A}} \right )\left ( \frac{2D _{A}}{D _{A}} \right )^{2}= \frac{4}{2}= \frac{2}{1}


Option 1)

2

This option is correct.

Option 2)

1

This option is incorrect.

Option 3)

1/2

This option is incorrect.

Option 4)

1/4

This option is incorrect.

N neha

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