Question

The following four wires are made of the same material and are at the same temperature. Which one of them has highest electrical resistance?

• A. Length $=50\text{cm}$,diameter$=0.5\text{mm}$
• B. Length $=100\text{cm}$, diameter$=1\text{mm}$
• C. Length$=200\text{cm}$, diameter$=2\text{mm}$
• D. Length $=300\text{cm}$, diameter$=3\text{mm}$

Answer 1

The correct option is A Length $=50\text{cm}$,diameter$=0.5\text{mm}$

Resistance,$R=\rho \frac{l}{A}=\rho \frac{l}{\frac{\pi d^2}{4}}$
For same material,
$R\propto \frac{l}{d^2}$

For highest resistance, the value of $\left(\frac{l}{d^2}\right)$ should be maximum, and it is maximum for option $\left(A\right)$

Hence, $\left(A\right)$ is the correct answer.