Question

If we double both the length and cross-sectional area of the wire, then its resistance will ____.

• A. remain the same
• B. increase by two times
• C. reduce by two times
• D. increase by four times

Answer 1

The correct option is A remain the same

Resistance is given by:
$R=\frac{\rho L}{A}$
where:
$\rho :$ Resistivity
$L:$ Length of the resistance
$A:$ Area of cross-section

When length and area of cross-section is double, let the new resistance be $R^{\prime }$.
$\frac{R^{\prime }}{R}=\frac{\rho \times 2L/2A}{\rho \times L/A}$
$⟹R^{\prime }=R$
That is, the resistance will not change.