Question

If the length of the wire is doubled and its area of cross section is decreased to half, then its resistance

• A. Will increases $4$ times
• B. Will become double
• C. Will remain the same as before
• D. Will become half the initial value

Answer 1

The correct option is A Will increases $4$ times

$\text{Step 1: Initial Resistance}$

$R=\rho \frac{\ell }{A}$

$\text{Step 2: Final Resistance}$

Final length ${\ell }^{\prime }=2\ell$

Final cross-section $A^{\prime }=\frac{A}{2}$

$\therefore R^{\prime }=\rho \frac{{\ell }^{\prime }}{A^{\prime }}=\frac{\rho .2\ell }{\frac{A}{2}}=4\rho \frac{\ell }{A}=4R$

Hence resistance will become $4$ times

Option A is correct.