Question

In an experiment, it was observed that when the length of a wire in an electrical circuit is doubled, everything else remaining same, the current becomes half. On the other hand, if the thickness (diameter) of the wire is doubled, the current becomes 4 times. Two wires $W_1$ and $W_2$ of the same metal have the same current passing through them. the thickness of wire $W_2$ is twice that of $W_1$ then the length of the wire $W_2$ is

• A. sixteen times that of $W_1$
• B. four times that of wire $W_1$
• C. two times that of wires $W_1$
• D. same as that of wire $W_1$

Answer 1

The correct option is B four times that of wire $W_1$

Both wire have the same current it means resistance of both wire is same

$R_1=R_2$

$\Rightarrow \rho \frac{l_1}{A_1}=\rho \frac{l_1}{A_1}$

$\to \frac{l_1}{A_1}=\frac{l_1}{A_1}$

Given, $d_2=2d_1$

hence, $l_2=4l1$