Statement I: A wire of uniform cross-section and uniform resistivity is connected across an ideal cell. Now the length of the wire is doubled keeping volume of the wire constant. The drift velocity of electrons after stretching the wire becomes one-fouth of what it was before stretching the wire.
Statement II: If a wire (of uniform resistivity and uniform cross section) of length `l_0` is stretched to length `nl_0`, then its resistance becomes `n^2` times of what it was before stretching the wire (the volume of wire is kept constant in stretching process). Further at constant potential difference, current is inversely proportional to resistance. Finally, drift velocity of free electron is directly proportional to current and inversely proportional to cross-sectional area of current carrying wire.

Options

A. Statement I is true, Statement II is True, Statement II is a correct explanation for Statement I.
B. Statement I is True, Statement II is True, Statement II is not a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Answer

D

Explanation

d. As the length of the wire is doubled, the cross-sectional
area of the wire becomes half. Therefore, resistance of
the wire becomes four times and the current beocmes one-
fourth of the initial value.
Also, `V_(d) = I/(neA)`
Since current becomes one-fourth and cross-sectional area of the
wire becomes half, from the above equation the drift velocity of
electron becomes half. Hence, Statement I is false.