Assertion :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-fourth of what it was before stretching the wire. Reason: If a wire (of uniform resistivity and uniform cross section) of length l0 is stretched to length nL0, then its resistance becomes n2 times of what it was before stretching the wire (the volume of wire is ept 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.
Assertion :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-fourth of what it was before stretching the wire. Reason: If a wire (of uniform resistivity and uniform cross section) of length l0 is stretched to length nL0, then its resistance becomes n2 times of what it was before stretching the wire (the volume of wire is ept 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.
The correct option is D Both Assertion and Reason are incorrect
As the length of the wire is doubled, the cross-sectional area of the wire becomes half. Therefore, the resistance of the wire becomes four times and the current becomes one-fourth of the initial value.
Also, Vd=IneA
Since current becomes one-fourth and cross-sectional area of the wire becomes half, therefore, from the above equation, the drift velocity of the electron becomes half. Hence, Statement I is false.
As the length of the wire is doubled, the cross-sectional area of the wire becomes half. Therefore, the resistance of the wire becomes four times and the current becomes one-fourth of the initial value.
Also, Vd=IneA
Since current becomes one-fourth and cross-sectional area of the wire becomes half, therefore, from the above equation, the drift velocity of the electron becomes half. Hence, Statement I is false.
