Question

Two copper wires have the same length, but one has twice the diameter of the other.

Compared to the one that has the smaller diameter, the one that has the larger diameter has a resistance that is...

a) the same
b) smaller by a factor of 1/4.
c) smaller by a factor of 1/2.
d) larger by a factor of 2.
e) larger by a factor of 4

Answer 1

Answer:

Option b. is correct.

Explanation:

We know, resistance is given by :

$R=\dfrac{\rho\ L}{A}=\dfrac{\rho\ L}{\pi r^2}$

Since, both the wires are made up of copper. Therefore , $\rho$ is same for both the resistance.

Now, one resistance has diameter double than other.

Therefore, its radius is also double than other.

Now, $R_1=\dfrac{\rho\ L}{\pi r^2}$

Then , $R_2=\dfrac{\rho\ L}{\pi (2r)^2}=\dfrac{1}{4}\times \dfrac{\rho\ L}{\pi r^2}=\dfrac{R}{4}$

Therefore, compared to the one that has the smaller diameter, the one that has the larger diameter has a resistance that is smaller by a factor of 1/4 .

Hence, this is the required solution.