Question

The length of the wire is doubled, Its conductance will

• A. remain unchanged
• B. be halved
• C. be doubled
• D. be quadrupled

Answer 1

Answer: (B)

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 $l_2=2l_1$, we get
${\sigma }_2=\frac{{\sigma }_1}{2}$
Therefore, conductance will be halved.