Question

The resistance of a wire of uniform diameter $d$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2d$ and length $4L$ will be

• A. $2R$
• B. $R$
• C. $R/2$
• D. $R/4$

Answer 1

Answer: (B)

$R$

Answer 2

$R \propto \frac{l}{A} \propto \frac{l}{d^{2}}$ ⇒ $\frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \left( \frac{d_{2}}{d_{1}} \right)^{2} = \frac{L}{4L}\left( \frac{2d}{d} \right)^{2} = 1$

⇒ R₂ = R₁ = R.