Physics

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 imes. 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 wire $$W_2$$ is


ANSWER

Four times that of wire $$W_1$$


SOLUTION
Both wire have the same current it means resistance of both wire is same.
$$R_1=R_2$$
$$\rho \frac {l_1}{A_1}=\rho \frac {l_2}{A_2}\Rightarrow \frac {l_1}{A_1}=\frac {l_2}{A_2}$$
given $$d_2-2d_1$$
Hence, $$l_1=4l_2$$
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