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  4. The length of the wire is doubled, Its conductance will

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Q. The length of the wire is doubled, Its conductance will

AFMCAFMC 2007Electromagnetic Induction

Solution:

Conductance is inverse of resistance.
Conductance is given by
$\sigma=\frac{1}{R}$
Substituting $R=\rho \frac{l}{A}$, we get
$\sigma=\frac{A}{\rho l}$
If $A=$ constant, then we have
$\sigma \propto \frac{1}{l} \Rightarrow \frac{\sigma_{2}}{\sigma_{1}}=\frac{l_{3}}{l_{2}}$
Substituting $l_{2}=2 l_{1}$, we get
$\sigma_{2}=\frac{\sigma_{1}}{2}$
Therefore, conductance will be halved.