Question

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

• A. Will increase 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 increase 4 times

we know that $R=\frac{\rho l}{A}$

$l^{\prime }=2l$

$A^{\prime }=\frac{A}{2}$

$R^{\prime }=\frac{\rho l^{\prime }}{A^{\prime }}=\frac{\rho \left(2l\right)}{\left(A/2\right)}$

$=4\frac{pl}{A}=4R$