Question

Assertion: If the length of the conductor is doubled, the drift velocity will become half of the original value (keeping potential difference unchanged).
Reason : At constant potential difference, drift velocity is inversely proportional to the length of the conductor.

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

We know that in a conductor, $J=n e V_{d}$
or $V_{d}=\frac{I}{n e A}$
$I=\frac{V}{R}$ and $R=\rho \frac{1}{A}$
So, the value of drift velocity becomes $V _{ d }=\frac{ V }{(\text { ne } \rho) l } \ldots \ldots \ldots$ (1)
From eq. 1 we can see $V _{ d }$ is inversely related to length 1 because voltage is given constant.
So, $V _{ d } \alpha \frac{1}{ L }$
Therefore, if we double the length of the conductor then it's drift velocity becomes half. Hence assertion is true.
And the reason is the correct explanation of the assertion.