Question

If the length and area of cross-section of a conductor are doubled, then its resistance will be

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

Answer 1

Answer: (A)

unchanged

We know that the resistance of wire of length $L$ and of cross section area $A$ is $R=\frac{\rho L}{A}$ where $\rho =$ resistivity of metal of the wire.

When length and cross section are doubled, the resistance becomes $R^{\prime }=\frac{\rho \left(2L\right)}{\left(2A\right)}=\frac{\rho L}{A}=R$