Question

Two wires A and B are made of copper. Both wires are 1 m long but wire A
is 2mm thick and wire B is 4 mm thick. The specific resistance is
1) more for A
2)
more for B
3) same for both A and BN
4) less for B as compared to A​

Answer 1

Given:-

length of both wires=1 m

diameter of wire A, $d_{A}$=2 mm

diameter of wire B, $d_{B}$=4 mm

To Find:-

specific resistance of two wires

Explanation:-

Resistance of wire is given by, R=$\dfrac{\rho\times L}{A}$ where,

$\rho=\text{specific resistance}\\\\L=\text{length of wire}\\\\A=\text{area of cross-section}=\dfrac{\pi\times d^{2}}{4}$

For same wire, $\rho$ and L is same.

$\Rightarrow\dfrac{R_{A}}{R_{B}}=\dfrac{d_{B}^{2}}{d_{A}^{2}}=\dfrac{2^{2}}{4^{2}}=\dfrac{1}{4}=0.25\\\\\Rightarrow\text{resistance is more for wire B than A}$